ELECTROMOTIVE FORCE E.M.F.

BACK TO ELECTROMOTIVE FORCE A BATTERY HAS AN E.M.F. OF V VOLTS IF IT MAINTAINS A CONSTANT POTENTIAL DIFFERENCE V BETWEEN ITS TERMINALS. IF THE TERMINALS ARE CONNECTED BY A CONDUCTOR OF RESISTANCE R A CURRENT V/R FLOWS AROUND THE CIRCUIT, MADE UP OF THE BATTERY AND THE EXTERNAL RESISTANCE. THE ELECTRIC FIELD IS EVERYWHERE STATIC AND THE LINE INTEGRAL OF THE FIELD e OVER ANY CLOSE LOOP IS ZERO. ON THE OTHER HAND, THE LINE INTEGRAL OF THE FIELD E OVER ANY PATH B/W POINT A AND B IS CONSTANT AND EQUAL TO THE POTENTIAL DIFFERENCE BETWEEN THE TWO POINTS. IF THE POINTS A AND B ARE THE POSITIVE AND NEGATIVE TERMINALS OF THE BATTERY, THE BATTERY E.M.F. IS GIVEN BY V = Φ(rA) - Φ(rB) = ∫ABE.dl Φ - ELECTROSTATIC POTENTIAL

GOD IS LOVE

LET US STUDY THE BIBLE TOGETHER – LOVE TEXT : 1 CORINTHIANS 13 1 Corinthians 13 King James Version (KJV) 13 Though I speak with the tongues of men and of angels, and have not charity, I am become as sounding brass, or a tinkling cymbal. 2 And though I have the gift of prophecy, and understand all mysteries, and all knowledge; and though I have all faith, so that I could remove mountains, and have not charity, I am nothing. 3 And though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing. 4 Charity suffereth long, and is kind; charity envieth not; charity vaunteth not itself, is not puffed up, 5 Doth not behave itself unseemly, seeketh not her own, is not easily provoked, thinketh no evil; 6 Rejoiceth not in iniquity, but rejoiceth in the truth; 7 Beareth all things, believeth all things, hopeth all things, endureth all things. 8 Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away. 9 For we know in part, and we prophesy in part. 10 But when that which is perfect is come, then that which is in part shall be done away. 11 When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things. 12 For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known. 13 And now abideth faith, hope, charity, these three; but the greatest of these is charity. Vs 1 WHEN I SPEAK WITHOUT LOVE IT IS SIMPLY NOISE VS 2 IF I AM VERY RELIGIOUS WITHOUT LOVE, IT MAKES ME NOTHING. VS 3 WHEN I GIVE ALMS AND DO PENANCE AND SUFFER AND DO GOOD DEEDS WITHOUT LOVE, THERE IS NO PROFIT. LOVE (CHARITY) IS IMPORTANT. LET US LOOK AT LOVE (CHARITY) WE NEED LOVE TO BE RELEVANT, AND HAVE WORTH, RELEVANCE, MEANING, GAIN IN ALL WE DO, OR PRACTICE OR SAY OR THINK. WHAT IS LOVE? LOVE IS PATIENT AND KIND LOVE SUFFERETH LONG LOVE = PATIENT = LONG SUFFERING. THIS MEANS THAT YOU BEAR UNPLEASANT SITUATIONS CALMLY, WITHOUT FRETING OR ANXIETY. LOVE = KIND THIS MEANS THAT YOU DO NICE THINGS FOR OTHERS , THIS MEANS THAT YOU ARE FAVOURABLY DISPOSED TOWARDS OTHERS. THIS MEANS THAT YOU ARE WILLING TO GO OUT OF YOUR WAY TO BE OF ASSISTANCE TO OTHERS. IT MEANS THAT YOU ARE WILLING TO HAVE SOME DISCOMFORT FOR THE COMFORT OF OTHERS. THIS MEANS THATYOU ARE COMPASSIONATE. THIS MEANS THAT YOU THINK GOOD OF OTHERS AND DO GOOD TO AND FOR OTHEERS. LET BROTHERLY LOVE CONTINUE. LOVE ENVIETH NOT VS 4 THIS MEANS THAT YOU ARE NOT UNCOMFORTABLE WHEN OTHERS ARE MAKING PROGRESS OR IF OTHERS ARE BETTER THAN WE ARE OR IF THINGS TURN OUT WELL FOR OTHERS LOVE VAUNTETH NOT ITSELF: LOVE IS NOT PROUD. LOVE IS HUMBLE LOVE IS NOT PUFFED UP LOVE IS HUMBLE VS 5 LOVE DOES NOT BEHAVE ITSELF UNSEEMINGLY LOVE BEHAVES WELL LOVE IS DESCENT LOVE IS RESPONSIBLE SEEKETH NOT HER OWN LOVE IS NOT SELFISH LOVE IS NOT EASILY PROVOKED. LOVE IS PATIENT WITH OTHERS LOVE IS FORGIVING LOVE HAS A FORGIVING SPIRIT LOVE BEARS AND FORBEARS. LOVE THINKETH NO EVIL, AND DOES NO EVIL YOU DO WHAT YOU THINK ABOUT. AS A MAN THINKETH, SO IS HE. WHEN YOU LOVE YOU THINK ONLY GOOD THOUGHTS. YOU THINK ONLY OF LOVLY THINGS YOU THINK ONLY OF THINGS THAT ARE OF GOOD REPORT. YOU THINK GOOD OF OTHERS. YOU THINK GODLY THOUGHTS. AS A MAN THINKETH, SO IS HE. WHEN YOU LOVE YOU THINK ONLY OF GOOD THINGS. VS 6 LOVE REJOICETH NOT IN INIQUITY BUT REJOICETH IN THE TRUTH. LOVE REJOICETH IN THE TRUTH VS 7 LOVE BEARETH ALL THINGS. THIS MAY SOUND DIFFICULT, HOWEVER GOD IS LOVE AND KNOWS ALL THINGS AND HENCE BELIEVES ALL THINGS . REMEMBER THAT ALL THE THINGS HE BELIEVES ARE TRUE AND RIGHT. ENDURANCE IS AN ATTRIBUTE OF LOVE AND GOD MAKES THIS POSSIBLE. IN THE WORLD YOU HAVE TRIBULATION; BE OF GOOD CHEER FOR I HAVE OVERCOME THE WORLD . THIS IS MADE POSSIBLE BY THE LOVE OF GOD THAT ENABLES US TO BEAR AND ENDURE HARDSHIP AND DIFFICULTIES AND TRINULATION AS A TRUE SOLDIER OF THE CROSS. WHEN YOU ENDURE WITHOUT COMMITTING SIN AND YOU STAY RIGHTEOUS, YOU WILL OVERCOME AND BE VICTOREOUS. VS 8 LOVE NEVER FAILS VS 13 LOVE IS T HE GREATEST GOD LOVES US WITH AN EVER LASTING LOVE JER. 31: 3 CANT 2:4 (SONGS OF SOLOMON) BANNER OVER ME WAS LOVE PROV 10: 12 LOVE COVERETH ALL SINS HOS 14:4 I WILL LOVE THEM FREELY SAYS GOD ALMIGHTY TO THIS PEOPLE. (WE ARE THE PEOPLE OF GOD IF WE BELIEVE IN HIS ONLY BEGOTTEN SON JESUS CHRIST AND LET THE SPIRIT OF GOD DWELL IN US RICHLY AND MAKE US TO KEEP HIS COMMANDMENTS) MIC 6:8 LOVE MERCY AND WALK HUMBLY MAT 5:44, LU6:27 JESUS CHRIST SAID, “LOVE YOUR ENEMIES” JN 15: 12, 17 THAT YE LOVE ONE ANOTHER (GOD WANTS US TO LOVE ONE ANOTHER) GOD WANTS US TO LOVE ONE ANOTHER ROM 13:8 OWE NO MAN ANYTHING, BUT TO LOVE GRACE BE TO ALL MEN THAT LOVE. 1 PETER 2:17 LOVE THE BROTHERHOOD REV 3:19 AS MANY AS I LOVE I REBUKE SAYS THE LORD GOD. OUR LORD JESUS CHRIST. THANK YOU AND GOD BLESS YOU.

LOVE

LET US STUDY THE BIBLE TOGETHER – LOVE TEXT : 1 CORINTHIANS 13 Vs 1 WHEN I SPEAK WITHOUT LOVE IT IS SIMPLY NOISE VS 2 IF I AM VERY RELIGIOUS WITHOUT LOVE, IT MAKES ME NOTHING. VS 3 WHEN I GIVE ALMS AND DO PENANCE AND SUFFER AND DO GOOD DEEDS WITHOUT LOVE, THERE IS NO PROFIT. LOVE (CHARITY) IS IMPORTANT. LET US LOOK AT LOVE (CHARITY) WE NEED LOVE TO BE RELEVANT, AND HAVE WORTH, RELEVANCE, MEANING, GAIN IN ALL WE DO, OR PRACTICE OR SAY OR THINK. WHAT IS LOVE? LOVE IS PATIENT AND KIND LOVE SUFFERETH LONG LOVE = PATIENT = LONG SUFFERING. THIS MEANS THAT YOU BEAR UNPLEASANT SITUATIONS CALMLY, WITHOUT FRETING OR ANXIETY. LOVE = KIND THIS MEANS THAT YOU DO NICE THINGS FOR OTHERS , THIS MEANS THAT YOU ARE FAVOURABLY DISPOSED TOWARDS OTHERS. THIS MEANS THAT YOU ARE WILLING TO GO OUT OF YOUR WAY TO BE OF ASSISTANCE TO OTHERS. IT MEANS THAT YOU ARE WILLING TO HAVE SOME DISCOMFORT FOR THE COMFORT OF OTHERS. THIS MEANS THATYOU ARE COMPASSIONATE. THIS MEANS THAT YOU THINK GOOD OF OTHERS AND DO GOOD TO AND FOR OTHEERS. LET BROTHERLY LOVE CONTINUE. LOVE ENVIETH NOT VS 4 THIS MEANS THAT YOU ARE NOT UNCOMFORTABLE WHEN OTHERS ARE MAKING PROGRESS OR IF OTHERS ARE BETTER THAN WE ARE OR IF THINGS TURN OUT WELL FOR OTHERS LOVE VAUNTETH NOT ITSELF: LOVE IS NOT PROUD. LOVE IS HUMBLE LOVE IS NOT PUFFED UP LOVE IS HUMBLE VS 5 LOVE DOES NOT BEHAVE ITSELF UNSEEMINGLY LOVE BEHAVES WELL LOVE IS DESCENT LOVE IS RESPONSIBLE SEEKETH NOT HER OWN LOVE IS NOT SELFISH LOVE IS NOT EASILY PROVOKED. LOVE IS PATIENT WITH OTHERS LOVE IS FORGIVING LOVE HAS A FORGIVING SPIRIT LOVE BEARS AND FORBEARS. LOVE THINKETH NO EVIL, AND DOES NO EVIL YOU DO WHAT YOU THINK ABOUT. AS A MAN THINKETH, SO IS HE. WHEN YOU LOVE YOU THINK ONLY GOOD THOUGHTS. YOU THINK ONLY OF LOVLY THINGS YOU THINK ONLY OF THINGS THAT ARE OF GOOD REPORT. YOU THINK GOOD OF OTHERS. YOU THINK GODLY THOUGHTS. AS A MAN THINKETH, SO IS HE. WHEN YOU LOVE YOU THINK ONLY OF GOOD THINGS. VS 6 LOVE REJOICETH NOT IN INIQUITY BUT REJOICETH IN THE TRUTH. LOVE REJOICETH IN THE TRUTH VS 7 LOVE BEARETH ALL THINGS. THIS MAY SOUND DIFFICULT, HOWEVER GOD IS LOVE AND KNOWS ALL THINGS AND HENCE BELIEVES ALL THINGS . REMEMBER THAT ALL THE THINGS HE BELIEVES ARE TRUE AND RIGHT. ENDURANCE IS AN ATTRIBUTE OF LOVE AND GOD MAKES THIS POSSIBLE. IN THE WORLD YOU HAVE TRIBULATION; BE OF GOOD CHEER FOR I HAVE OVERCOME THE WORLD . THIS IS MADE POSSIBLE BY THE LOVE OF GOD THAT ENABLES US TO BEAR AND ENDURE HARDSHIP AND DIFFICULTIES AND TRINULATION AS A TRUE SOLDIER OF THE CROSS. WHEN YOU ENDURE WITHOUT COMMITTING SIN AND YOU STAY RIGHTEOUS, YOU WILL OVERCOME AND BE VICTOREOUS. VS 8 LOVE NEVER FAILS VS 13 LOVE IS T HE GREATEST GOD LOVES US WITH AN EVER LASTING LOVE JER. 31: 3 CANT 2:4 (SONGS OF SOLOMON) BANNER OVER ME WAS LOVE PROV 10: 12 LOVE COVERETH ALL SINS HOS 14:4 I WILL LOVE THEM FREELY SAYS GOD ALMIGHTY TO THIS PEOPLE. (WE ARE THE PEOPLE OF GOD IF WE BELIEVE IN HIS ONLY BEGOTTEN SON JESUS CHRIST AND LET THE SPIRIT OF GOD DWELL IN US RICHLY AND MAKE US TO KEEP HIS COMMANDMENTS) MIC 6:8 LOVE MERCY AND WALK HUMBLY MAT 5:44, LU6:27 JESUS CHRIST SAID, “LOVE YOUR ENEMIES” JN 15: 12, 17 THAT YE LOVE ONE ANOTHER (GOD WANTS US TO LOVE ONE ANOTHER) GOD WANTS US TO LOVE ONE ANOTHER ROM 13:8 OWE NO MAN ANYTHING, BUT TO LOVE GRACE BE TO ALL MEN THAT LOVE. 1 PETER 2:17 LOVE THE BROTHERHOOD REV 3:19 AS MANY AS I LOVE I REBUKE SAYS THE LORD GOD. OUR LORD JESUS CHRIST. THANK YOU AND GOD BLESS YOU.

GOD LOVES US, THAT IS WHY HE WANTS US TO BE BORN AGAIN

GOD LOVES US, THAT IS WHY HE WANTS US TO BE BORN AGAIN 1 JOHN 4:7-8 BELOVETH LET US LOVE ONE ANOTHER FOR LOVE IS OF GOD, AND EVERY ONE THAT LOVETH IS BORN OF GOD AND KNOWETH GOD HE THAT LOVETH NOT KNOWETH NOT GOD; FOR GOD IS LOVE VS 9 IN THIS WAS MANIFESTED THE LOVE OF GOD TOWARD US, BECAUSE THAT GOD SENT HIS ONLY BEGOTTEN SON INTO THE WORLD THAT WE MIGHT LIVE. VS 10 HERE IN IS LOVE, NOT THAT WE LOVED GOD, BUT THAT HE LOVED US, AND SENT HIS SON TO BE THE PROPITIATION FOR OUR SINS. VS 11 BELOVED IF GOD SO LOVED US, WE OUGHT ALSO TO LOVE ONE ANOTHER VS 12 NO MAN HATH SEEN GOD AT ANY TIME. IF WE LOVE ONE ANOTHER , GOD DWELLETH IN US, AND HIS LOVE IS PERFECTED IN US. 1 JOHN 3:1 BEHOLD WHAT MANNER OF LOVE THE FATHER HATH BESTOWED UPON US, THAT WE SHOULD BE CALLED THE SONS OF GOD. THEREFORE THE WORLD KNOWETH US NOT, BECAUSE IT KNEW HIM NOT. VS 2 BEHOLD, NOW ARE WE THE SONS OF GOD, AND IT DOTH NOT YET APPEAR WHAT WE SHALL BE: BUT WE KNOW THAT, WHEN HE SHALL APPEAR, WE SHALL BE LIKE HIM; FOR WE SHALL SEE HIM AS HE IS. VS 3 AND EVERY MAN THAT HATH THIS HOPE IN HIM PURIFIETH HIMSELF, EVEN AS HE IS PURE. VS 4 WHOSOEVER COMMITTETH SIN TRANSGRESSETH ALSO THE LAW: FOR SIN IS THE TRANSGRESSION OF THE LAW. VS 5 AND YE KNOW THAT HE WAS MANIFESTED TO TAKE AWAY OUR SINS; AND IN HIM IS NO SIN. VS 8 JESUS CHRIST CAME TO DESTROY THE WORKS OF THE DEVIL. VS 9 WHOSOEVER IS BORN OF GOD DOTH NOT COMMIT SIN FOR HIS SEED REMAINETH IN HIM : AND HE CANNOT SIN BECAUSE HE IS BORN OF GOD. 1 JOHN 3:22 AND WHATSOEVER WE ASK, WE RECEIVE OF HIM, BECAUSE WE KEEP HIS COMMANDMENTS, AND DO THOSE THINGS THAT ARE PLEASING IN HIS SIGHT. VS 23 AND THIS IS HIS COMMANDMENT, THAT WE SHOULD BELIEVE ON THE NAME OF HIS SON JESUS CHRIST, AND LOVE ONE ANOTHER AS HE GAVE US COMMANDMENT VS 24 AND HE THAT KEEPETH HIS COMMANDMENTS DWELLETH IN HIM, AND HE IN HIM. AND HEREBY WE KNOW THAT HE ABIDETH IN US, BY THE SPIRIT WHICH HE HATH GIVEN US. 1 JOHN 4:1 BELOVED BELIEVE NOT EVERY SPIRIT BUT TRY THE SPIRIT WHETHER THEY ARE OF GOD BECAUSE MANY FALSE PROPHETS ARE GONE OUT INTO THE WORLD. VS 2 EVERY SPIRIT THAT CONFESSETH THAT JESUS CHRIST IS COME IN THE FLESH IS OF GOD. VS 3 YE ARE OF GOD ----- YE OVERCOME BECAUSE ---- GREATER IS CHRIST IN YOU.

POTENTIAL ENERGY IN ELECTROMAGNETIC FIELDS AND WAVES

POTENTIAL ENERGY IN ELECTROMAGNETIC FIELDS AND WAVES WE SHALL CONTINUE FROM OUR EARLIER DISCUSSION. HENCE; THE POTENTIAL ENERGY IS A FUNCTION OF POSITION, AND AT A POINT WITH POSITION VECTOR r, IT MAY BE WRITTEN AS qt Φ(r) THE FUNCTION Φ(r) IS CALLED THE ELECTROSTATIC POTENTIAL HENCE THEPOTENTIAL ENERGY DIFFERENCE B/W B AND A BECOMES qt Φ(rB) - qt Φ(rA) = -qt∫ABE.dl DIVIDING BY q Φ(rB) - Φ(rA) = -∫ABE.dl THE CHOICE OF THE ZERO POTENTIAL IS SIMPLY A MATTER OF CONVINIENCE. FOR AN ISOLATED SYSTEM OF CHARGES, IT IS USUAL FOR THE POTENTIAL AT INFINITY TO BE CHOSEN AS ZERO. FOR AN ISOLATED POINT CHARGE , SITUATED AT THE ORIGIN, THE POTENTIAL Φ(r) IS FOUND FOM THE WORK DONE IN BRINGING UP A TEST CHARGE qt FROM INFINITY TO THE POINT WITH POSITION VECTOR r. THE WORK DEPENDS ONLY ON THE MAGNITUDE r OF THE VECTOR r. qt Φ(r) - qt Φ(∞) = ∫∞r(qtqdr)/(4πε0r) = (qtq)/(4πε0r) TAKING Φ(∞) TO BE ZERO Φ(r) = (q)/(4πε0r) THE DIMENSIONS OF POTENTIAL ARE ENERGY PER UNIT CHARGE. THE UNIT OF POTENTIAL IS THE VOLT. ONE JOULE OF WORK IS DONE WHEN A CHARGE OF ONE COULOMB IS MOVED THROUGH A POTENTIAL DIFFERENCE OF ONE VOLT.

GOD IS LOVE

GOD IS LOVE GOD = LOVE GOD EQUALS LOVE GOD EQUAL TO LOVE ATTRIBUTES OR CHARACTERISTICS OF GOD ATTRIBUTES OR CHARACTERISTICS OF LOVE LOVE IS OF GOD GOD LOVES GOD MAKES US TO LOVE LOVE IS WHAT YOU ARE. LOVE IS WHAT YOU DO LOVE IS A NOUN AND A VERB WHEN YOU LOVE, YOU SHOW GOD’S QUALITY IN YOU. LOVE HAS TO BE GODLY TO BE LOVE ANYTHING ELSE IS NOT WITHOUT GOD YOU CANNOT LOVE WHEN YOU LOVE YOU GIVE FOR GOD SO LOVED THE WORLD THAT HE GAVE HIS ONLY BEGOTTEN SON LOVE IS PATIENT LOVE IS KIND LOVE BEARS ALL THINGS LOVE FORGIVES THE SPIRIT OF GOD IN YOU MAKES YOU TO LOVE LOVE IS AN ATTRIBUTE OF GOD. LOVE IS A CHARACTERISTIC OF GOD LOVE IS A QUALITY OF GOD ANYTHING THAT IS NOT GODLY IS NOT LOVE LOVE IS HOLY GOD IS HOLY GOD IS TRUE GOD IS PURE GOD IS LOVE, HOLY, PURE AND TRUE CHRIST IS LORD GOD AND SAVIOUR THE LORD GOD ALMIGHTY IS GOD GOD IS GOOD. GOD = LOVE = HOLY = PURE = TRUE = JESUS CHRIST = LORD = SAVIOUR LOVE IS NOT TO BE TOILED WITH. LOVE IS A STRONG FORCE, LOVE ABIDES FOR EVER. ALL OTHER THINGS WILL PASS AWAY. LOVE IMPROVES AND MAKES PERFECT ANY THING IT COMES IN CONTACT WITH. LOVE MAKES IT POSSIBLE TO PLEASE GOD. LOVE IS EVIDENCE OF AN INDWELLING CHRIST. LOVE MAKES IT POSSIBLE TO PUT THE FLESH IN CHECK AND CONTROL THE EMOTIONS AT ALL TIMES. LOVE MAKES IT POSSIBLE TO DO WHAT IS RIGHT EVEN WHEN IT HURTS. LOVE OVERCOMES ALL. LOVE MAKES IT POSSIBLE TO SAY PLEASE, SORRY AND THANK YOU; EVEN WHEN YOU ARE THE STRONGEST OF ALL AND THE RIGHTEOUS ONE. LOVE MAKES YOU HOLY AND RIGHTEOUS. LOVE MAKES YOU A FRIEND OF GOD. LOVE MAKES YOU A CHILD OF GOD LOVE MAKES YOU TO OBEY GOD LOVE MAKES YOU TO PLEASE GOD. LOVE MAKES IT POSSIBLE TO RECEIVE THE LOVE OF GOD. GOD LOVES US SO MUCH THAT WE TOO MAY LOVE HIM THE WAY HE DOES AND LOVE ONE ANOTHER. PERFECT LOVE CAST OUT FEAR. LOVE HELPS THE WEAK AND ENCOURAGES THE FEEBLE HAND. LOVE HELPS THE POOR LOVE MAKETH STRONG LOVE REJOICETH AT THE TRUTH AND UPHOLDETH JUSTICE. LOVE FORGIVES AND SHOWS MERCY. LOVE BRINGS ABOUT COMPASSION LOVE IS NOT EASY, HOWEVER LOVE MAKES DIFFICULTIES EASY. GOD IS LOVE LOVE GIVES ALL. LOVE STOPS US FROM COMMITTING SIN. FOR GREATER LOVE HAS NO MAN THAN THIS THAT A MAN SHALL LAY DOWN HIS LIFE FOR HIS FRIENDS. WHILE WE WERE YET SINNERS CHRIST DIED FOR US. JESUS CHRIST SAID, MY LITTLE CHILDREN, LOVE ONE ANOTHER. JN15:13 THOU SHALL LOVE THY ENEMIES THOU SHALL LOVE THY NEIGHBOUR. YOU ARE FREE TO DO WHAT YOU LIKE BUT YOU ARE NOT FREE TO CHOOSE THE RESULT OR OUTCOME OF WHAT YOU HAVE DONE. EVERY ACT OF LOVE SHALL BE REWARDED BY GOD. BE CAREFUL AND WISE WHEN YOU CHOOSE WHAT YOU SAY, THINK, OR DO BECAUSE ONCE THE CHOICE IS MADE, THE RESULT CAN NOT BE CHANGED. CHOOSE JESUS CHRIST TODAY AND YOUR FUTURE IS SURE. BELIEVE IN OUR LORD JESUS CHRIST TODAY AND YOU SHALL BE SAVED. THANK YOU AND GOD BLESS YOU.

ELECTROMAGNETIC INDUCTION AND MAGNETIC ENERGY

ELECTROMAGNETIC INDUCTION AND MAGNETIC ENERGY MAGNETOSTATICS MAGNETOSTATICS - IS THE MAGNETIC EFFECTS WHICH ARISE WHEN STEADY CURRENT FLOWS. ELECTROMAGNETIC INDUCTION IN ELECTROMAGNETIC INDUCTION, WE SHALL INVESTIGATE AND RELATE THE ELECTRIC FIELD TO THE CHANGING MAGNETIC FIELD. ELECROMOTIVE FORCE (EMF) CONSIDER THE TEST CHARGE qt which is moved in the field of a point charge q along the path AB If both charges are positive, work is done by the repulsive electrostatic force as the charge moves from A to B. Work done along the infinitesimal section dl of the path is qt x (magnitude of the field E)x(component of dl along the direction of E) = qtEdlcosθ = qtEdr = (qtqdr)/(4πε0r2) Total work done moving the test charge from A to B is ∫AB qtEdlcosθ = (qtq)/(4π ε0)∫r1r2 (dr)/(r2) = ((qtq)/(4π ε0)){(1/r1) – (1/r2)} Note that dot product can be used to express Edlcosθ as E.dl HENCE Work done = qt∫ABE.dl ∫ABE.dl ≡ Line integral of the field E along AB. The line integral is independent of the path b/w A and B The electro static field is conservative. In any electrostatic field E, the Line integral ∫ABE.dl has a constant value independent of the path joining the points A and B

MAXWELL'S EQUATIONS AND THE CONTINUITY EQUATION

THIS IS MAXWELL’S EQUATION These are equations which the field vectors E,D,B and H everywhere Satisfy. These equations are called Maxwell’s equation They are div D =ρf div B =0 Curl E = -dB/dt Curl H = jf + dD/dt Any possible electromagnetic field must satisfy all of Maxwell’s equation Consider the following equations Div D = ρf Curl H = jf + (𝜕D/𝜕t) These are part of Maxwell’s equation and can be combined to yield the continuity equation given below: (𝜕ρ/𝜕t) + div j =0 This is the continuity equation Consider the following identities such that for any Vector Field F div.Curl F ≡ 0 ∇.(∇^F) ≡ 0 ∇.(∇XF) ≡ 0 Applying this in the two equations above, [ the two Maxwell’s equations of interest] We have Div Curl H = div jf + div (𝜕D/𝜕t) We get this by taking the divergence of both sides of the equation So that Div Curl H = div jf + div (𝜕D/𝜕t) 0 = Div Curl H = div jf + div (𝜕D/𝜕t) {*} Differentiate the second of the Maxwell’s equation of interest and substituting in the other one (the first ie the one used earlier on;) We have: (𝜕divD/𝜕t) = (𝜕ρf/𝜕t) {**} This result in eqn {**} is then substituted in eqn {*} Ie subs for (𝜕divD/𝜕t) in * to yield 0 = div j + (𝜕ρ/𝜕t) This is the continuity equation. This shows that the continuity equation is embedded in the Maxwells equation This means that the Continuity equation can be derived from the Maxwells equation. This means that the Continuity equation is taken care of in Maxwell’s equation. HENCE ONE CAN SAY OF MAXWELL’S EQUATION THAT : Any possible electromagnetic field must satisfy all of Maxwell’s equation These are equations which the field vectors E,D,B and H everywhere Satisfy.

MORE ANALYTICAL TOOLS

Divergence of a vector Field. Let V(x,y,z) be a differentiable Vector function where x,y,z are Cartesian coordinates in space. Let V1, V2, V3 be the components of V Therefore Div V = (δV1/δx) + (δV2/δy) + (δV3/δz) This is the divergence of V or the divergence of the vector field defined by V Divergence of V is ∇.V = (δ/δx)i + (δ/δy)j + (δ/δz)k . (V1i + V2yj + V3k) = (δV1/δx) + (δV2/δy) + (δV3/δz) Note that (δ/δx)V1 in dot product means partial derivative (δV1/δx) This is just a convenient notation and nothing more. ∇.V means the scalar div V Where as ∇f means the vector grad f Eg V = 4xyi + 5zyj – xz2k Div V = 4y + 5z – 2xz If f (x,y,z) is a twice differentiable scalar function, grad f = (δf/δx)i + (δf/δy)j + (δf/δz)k since div V = (δV1/δx)i + (δV2/δy)j + (δV3/δz)k then div V (grad f) = (δ2f/δx2)i + (δ2f/δy2)j + (δ2f/δz2)k the expression on the right is the Laplacian of f Hence div V (grad f) = (δ2f/δx2)i + (δ2f/δy2)j + (δ2f/δz2)k = ∇2f CURL OF A VECTOR FIELD LET x,y,z be right – handed Cartesian Coordinates in space, and let V(x,y,z) = V1i + V2j + V3k Be or is a twice differentiable vector function The function Curl V = ∇ X V = | i j k | | (δ/δx) (δ/δy) (δ/δz) | | V1 V2 V3 | = ((𝜕V3/𝜕y) – (𝜕V2/𝜕z))i + ((𝜕V1/𝜕z) – (𝜕V3/𝜕x))j + ((𝜕V2/𝜕x) – (𝜕V1/𝜕y))k This is called the curl of the vector function V or the Curl of the vector field defined by V Invariance of the Curl The Length and direction of Curl V are independent of the particular choice of Cartesian Coordinate system in space.

THE CHURCH

The Church’s one foundation Is Jesus Christ her Lord, She is His new creation By water and the Word. From heaven He came and sought her To be His holy bride; With His own blood He bought her And for her life He died. She is from every nation, Yet one o’er all the earth; Her charter of salvation, One Lord, one faith, one birth; One holy Name she blesses, Partakes one holy food, And to one hope she presses, With every grace endued. The Church shall never perish! Her dear Lord to defend, To guide, sustain, and cherish, Is with her to the end: Though there be those who hate her, And false sons in her pale, Against both foe or traitor She ever shall prevail. Though with a scornful wonder Men see her sore oppressed, By schisms rent asunder, By heresies distressed: Yet saints their watch are keeping, Their cry goes up, “How long?” And soon the night of weeping Shall be the morn of song! ’Mid toil and tribulation, And tumult of her war, She waits the consummation Of peace forevermore; Till, with the vision glorious, Her longing eyes are blest, And the great Church victorious Shall be the Church at rest. Yet she on earth hath union With God the Three in One, And mystic sweet communion With those whose rest is won, With all her sons and daughters Who, by the Master’s hand Led through the deathly waters, Repose in Eden land. O happy ones and holy! Lord, give us grace that we Like them, the meek and lowly, On high may dwell with Thee: There, past the border mountains, Where in sweet vales the Bride With Thee by living fountains Forever shall abide!

HOLINESS

Romans 12 King James Version (KJV) 12 I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service. 2 And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God. 3 For I say, through the grace given unto me, to every man that is among you, not to think of himself more highly than he ought to think; but to think soberly, according as God hath dealt to every man the measure of faith. 4 For as we have many members in one body, and all members have not the same office: 5 So we, being many, are one body in Christ, and every one members one of another. 6 Having then gifts differing according to the grace that is given to us, whether prophecy, let us prophesy according to the proportion of faith; 7 Or ministry, let us wait on our ministering: or he that teacheth, on teaching; 8 Or he that exhorteth, on exhortation: he that giveth, let him do it with simplicity; he that ruleth, with diligence; he that sheweth mercy, with cheerfulness. 9 Let love be without dissimulation. Abhor that which is evil; cleave to that which is good. 10 Be kindly affectioned one to another with brotherly love; in honour preferring one another; 11 Not slothful in business; fervent in spirit; serving the Lord; 12 Rejoicing in hope; patient in tribulation; continuing instant in prayer; 13 Distributing to the necessity of saints; given to hospitality. 14 Bless them which persecute you: bless, and curse not. 15 Rejoice with them that do rejoice, and weep with them that weep. 16 Be of the same mind one toward another. Mind not high things, but condescend to men of low estate. Be not wise in your own conceits. 17 Recompense to no man evil for evil. Provide things honest in the sight of all men. 18 If it be possible, as much as lieth in you, live peaceably with all men. 19 Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord. 20 Therefore if thine enemy hunger, feed him; if he thirst, give him drink: for in so doing thou shalt heap coals of fire on his head. 21 Be not overcome of evil, but overcome evil with good. HOLINESS WHAT IS HOLINESS? BEING WITHOUT SIN HOW IS IT ACHIEVED? LET IN CHRIST JESUS TO TAKE OUT SIN WHAT HAPPENS THEN? YOU LIVE FOR HIM WHO SAVED YOU AND SET YOU FREE FROM THE BONDAGE OF SIN. SIN HOLDS PEOPLE CAPTIVE SIN IS A BOND. RIGHTEOUSNESS IS OF GOD. LET US TAKE A LOOK AT THE WORD OF GOD ROMANS CHAPTER 12 VS 1 I BESEECH YOU . ----- HE IS TRYING TO COMPASSIONATELY PLEAD WITH US BECAUSE IT IS IN OUR OWN INTEREST. THIS IS WHAT GOD DEMANDS AND THIS WHAT IS ACCEPTABLE TO HIM AND THIS IS OUR REASONABLE SERVICE. [HOLINESS] VS 2 DO NOT CONFORM TO THIS WORLD. DO NOT BE TRENDY OR BE LIKE OTHERS. [THIS WILL AFFECT YOUR HOLINESS] VS 3 THEN YOU WILL PROVE WHAT IS GOOD AND ACCEPTABLE AND PERFECT WILL OF GOD. EG. IF YOU LIVE A RIGHTEOUS AND HOLY LIFE, YOU WILL PROVE THAT IT IS THE WILL OF GOD ESPECIALLY WHEN YOU OVERCOME AND HAVE VICTORY AND SUCCEED IN YOUR ENDEVOUR. VS 3 DO NOT BE PROUD. BE SOBER BASED ON YOUR FAITH VS 6 USE THE GIFT OF GOD ACCORDING TO THE GRACE GIVEN TO YOU. ANYTHING YOU DO, DO IT WELL VS 7 -9 MINISTRY (SERVICE TO OTHERS) TEACHING EXHORTATION RULE (WITH DILIGENCE) SHOW MERCY CHEERFULLY LOVE WITHOUT DISSIMULATION VS 9 ABHORE THAT WHICH IS EVIL CLEAVE TO THAT WHICH IS GOOD VS 10 BE KINDLY AFFECTIONED ONE TO ANOTHER WITH BROTHERLY LOVE; IN HONOUR PREFERRING ONE VS 11 NOT SLOTHFUL IN BUSINESS, FERVENT IN SPIRIT SERVING THE LORD VS 12 REJOICING IN HOPE; PATIENT IN TRIBULATION CONTINUING INSTANT IN PRAYER VS 13 DISTRIBUTING TO THE NECESSITY OF SAINTS GIVEN TO HOSPITALITY VS 14 BLESS THEM WHICH PERSECUTE YOU; BLESS AND CAUSE NOT VS 15 REJOICE WITH THEM THAT DO REJOICE AND WEEP WITH THEM THAT WEEP VS 16 BE OF THE SAME MIND ONE TOWARD ANOTHER MIND NOT HIGH THINGS, BUT CONDESCEND TO MEN OF LOW ESTATE. BE NOT WISE IN YOUR OWN CONCEITS. [BE HUMBLE] VS 17 RECOMPENSE TO NO MAN EVIL FOR EVIL PROVIDE THINGS HONEST IN THE SIGHT OF ALL MEN VS 18 AS MUCH AS POSSIBLE LIVE PEACEABLY WITH ALL MEN VS 19 AVENGE NOT YOURSELVES GIVE PLACE TO WRATH VENGEANCE IS MINE SAITH THE LORD VS 20 IF YOUR ENEMY HUNGER FEED HIM IF HE THIRST GIVE HIM DRINK VS 21 BE NOT OVERCOME OF EVIL, BUT OVERCOME EVIL WITH GOOD. BELIEVE IN OUR LORD JESUS CHRIST TODAY AND YOU SHALL BE SAVED. YOU AND YOUR HOUSEHOLD SHALL BE SAVED. WHEN JESUS CHRIST COMES IN SIN GOES OUT. WHEN LIGHT COMES IN DARKNESS GOES OUT. JESUS CHRIST IS THE LIGHT OF THE WORLD. IN HIM IS NO DARKNESS AT ALL.

ANALYTICAL TOOLS

VECTORS AND VECTOR ANALYSIS A DIRECTED LINE SEGMENT IS CALLED A VECTOR. THE LENGTH IS CALLED THE LENGTH OF THE VECTOR. AND THE DIRECTION IS CALLED THE DIRECTION OF THE VECTOR. TWO VECTORS ARE EQUAL IF AND ONLY IF THEY HAVE THE SAME LENGTH AND THE SAME DIRECTION. THE LENGTH OF A VECTOR IS CALLED THE EUCLIDEAN NORM OR MAGNITUDE. INNER PRODUCT(DOT PRODUCT) THIS IS ALSO CALLED SCALAR PRODUCT THE RESULT IS A SCALAR a.b = |a||b|cosϒ for a=/= 0, b=/= 0 a.b = 0 a=0 or b=0 and ϒ(0<ϒ<π) IS ANGLE B/W a&b THIS IS COMPUTED WHEN THE VECTORS HAVE THEIR INITIAL POINT COINCIDING. VECTOR PRODUCT ( CROSS PRODUCT) THE RESULT IS A VECTOR Axb (or a^b) v = axb = 0 THIS IS THE CASE IF AND ONLY IF THE VECTORS a AND b HAVE THE SAME OR OPPOSITE DIRECTION OR ONE OF THESE VECTORS IS THE ZERO VECTOR. IN ANY OTHER CASE, v = axb LENGTH = AREA OF PARALLELOGRAM WHOSE SIDES ARE a & b. DIRECTION = PERPENDICULAR TO BOTH a AND b a,b,v FORM A RIGHT HANDED TRIPLE OR RIGHT HANDED TRIAD |v|=|a||b|sinϒ DIRECTIONAL DERIVATIVE THE CONCEPT OF DIRECTIONAL DERIVATIVE HAS TO DO WITH THE DIFFERENTIATION OF A FUNCTION OR A VECTOR FIELD IN A PARTICULAR DIRECTION. THIS GIVES YOU THE RATE OF CHANGE OF THE FUNCTION OR VECTOR FIELD WITH RESPECT TO A GIVEN VARIABLE IN A PARTICULAR DIRECTION. CONSIDER A POINT P IN SPACE AND A DIRECTION AT P GIVEN BY A UNIT VECTOR b LET C BE A RAY AT P IN THE DIRECTION OF b LET Q BE A POINT ON C WHOSE DISTANCE FROM P IS S δf/δs = lim {f(Q) – f(P)}/s s0 s = distance between P and Q IF THE LIMIT EXISTS, IT IS CALLED THE DIRECTIONAL DERIVATIVE OF F AT P IN THE DIRECTION OF b. δf/δs is written as Dbf D = differentiation b= indicates direction From this there are infinitely many directional derivatives of f at P each corresponding to a different direction. Using Cartesian Coordinate system, we may repent the derivative terms of the first partial derivative of f at P in the following manner; If P has a position vector a, The ray C can be represented in the form r(s) = x(s)i + y(s)j + z(s)k (*) = a + sb Where a is the position vector of P s is the distance between P and Q b is the unit vector showing the direction of the ray C therefore δf/δs is the derivative of the function f[x(s),y(s),z(s)] with respect to the arc length s of C Applying the chain rule and assuming that the function f has continuous first partial derivatives δf/δs = (δf/δx)(x’) + (δf/δy)(y’) + (δf/δz)(z’) (‘) denotes derivatives with respect to s and evaluated at s =0 From equation (*) r ’ = X’i + y’j + z’k = b we can introduce the vector grad f = (δf/δx)i + ( δf/δy)j + ( δf/δz)k Using the concept of dot product δf/δs = b.gradf The vector grad f is called the gradient of the scalar f Consider a differential operator V = (δ/δx)i + (δ/δy)j + (δ/δz)k V is called nabla or del grad f = (δf/δx)i + ( δf/δy)j + ( δf/δz)k grad f = (δf/δx)i + ( δf/δy)j + ( δf/δz)k if b has the direction of the positive x axis, then b = i and δf/δs = b. grad f = (δf/δx)i.i = δf/δx Similarly the directional derivative in the positive y-direction is ( δf/δy) etc. Let f(P) = f(x,y,z) be a scalar function having continuous first partial derivatives. Then grad f exists and its length and direction are independent of the particular choice of Cartesian coordinates in space. If at a point P the gradient of “f” is not the zero vector, it has the direction of maximum increase of “f” at P. MAXWELL’S EQUATIONS THESE ARE EQUATIONS WHICH THE FIELDS { E,D,B & H } EVERYWHERE SATISFY.

JESUS CHRIST SAVES AND FORGIVES US OUR SINS

LET US STUDY THE BIBLE TOGETHER TODAY TEXT MARK 2:1-5 TOPIC: JESUS CHRIST FORGIVES US OUR SINS Mark 2 King James Version (KJV) 2 And again he entered into Capernaum after some days; and it was noised that he was in the house. 2 And straightway many were gathered together, insomuch that there was no room to receive them, no, not so much as about the door: and he preached the word unto them. 3 And they come unto him, bringing one sick of the palsy, which was borne of four. 4 And when they could not come nigh unto him for the press, they uncovered the roof where he was: and when they had broken it up, they let down the bed wherein the sick of the palsy lay. 5 When Jesus saw their faith, he said unto the sick of the palsy, Son, thy sins be forgiven thee. 6 But there was certain of the scribes sitting there, and reasoning in their hearts, 7 Why doth this man thus speak blasphemies? who can forgive sins but God only? 8 And immediately when Jesus perceived in his spirit that they so reasoned within themselves, he said unto them, Why reason ye these things in your hearts? 9 Whether is it easier to say to the sick of the palsy, Thy sins be forgiven thee; or to say, Arise, and take up thy bed, and walk? 10 But that ye may know that the Son of man hath power on earth to forgive sins, (he saith to the sick of the palsy,) 11 I say unto thee, Arise, and take up thy bed, and go thy way into thine house. 12 And immediately he arose, took up the bed, and went forth before them all; insomuch that they were all amazed, and glorified God, saying, We never saw it on this fashion. 13 And he went forth again by the sea side; and all the multitude resorted unto him, and he taught them. 14 And as he passed by, he saw Levi the son of Alphaeus sitting at the receipt of custom, and said unto him, Follow me. And he arose and followed him. 15 And it came to pass, that, as Jesus sat at meat in his house, many publicans and sinners sat also together with Jesus and his disciples: for there were many, and they followed him. 16 And when the scribes and Pharisees saw him eat with publicans and sinners, they said unto his disciples, How is it that he eateth and drinketh with publicans and sinners? 17 When Jesus heard it, he saith unto them, They that are whole have no need of the physician, but they that are sick: I came not to call the righteous, but sinners to repentance. 18 And the disciples of John and of the Pharisees used to fast: and they come and say unto him, Why do the disciples of John and of the Pharisees fast, but thy disciples fast not? 19 And Jesus said unto them, Can the children of the bridechamber fast, while the bridegroom is with them? as long as they have the bridegroom with them, they cannot fast. 20 But the days will come, when the bridegroom shall be taken away from them, and then shall they fast in those days. 21 No man also seweth a piece of new cloth on an old garment: else the new piece that filled it up taketh away from the old, and the rent is made worse. 22 And no man putteth new wine into old bottles: else the new wine doth burst the bottles, and the wine is spilled, and the bottles will be marred: but new wine must be put into new bottles. 23 And it came to pass, that he went through the corn fields on the sabbath day; and his disciples began, as they went, to pluck the ears of corn. 24 And the Pharisees said unto him, Behold, why do they on the sabbath day that which is not lawful? 25 And he said unto them, Have ye never read what David did, when he had need, and was an hungred, he, and they that were with him? 26 How he went into the house of God in the days of Abiathar the high priest, and did eat the shewbread, which is not lawful to eat but for the priests, and gave also to them which were with him? 27 And he said unto them, The sabbath was made for man, and not man for the sabbath: 28 Therefore the Son of man is Lord also of the sabbath. LET US TAKE A LOOK AT THE PASSAGE IN SOME CONSIDERABLE DETAIL VS 1JESUS CHRIST ENTERED CAPERNAUM NEWS WENT ROUND WHEN YOU ARE A CHRISTIAN, NEWS WILL GO ROUND THAT YOU ARE IN TOWN. NEWS WILL GO ROUND THAT JESUS CHRIST IN YOU IS IN TOWN. BY THEIR FRUITS WE SHALL KNOW THEM. YOU CANNOT HIDE JESUS CHRIST. JESUS CHRIST WENT ABOUT DOING GOOD. VS 2 MANY CAME TOGETHER, AND HE PREACHED THE WORD UNTO THEM. WHEN PEOPLE COME TO YOU OR WHEN YOU YOU MEET PEOPLE DO YOU PREACH THE WORD UNTO THEM? THE WORD OF GOD IS WHAT PEOPLE NEED TO BE SAVED. PEOPLE CAME TO JESUS CHRIST BECAUSE OF WHAT THEY WANTED , AND JESUS CHRIST GAVE THEM WHAT THEY NEEDED MOST AND THEY WERE SATISFIED. DO YOU GIVE PEOPLE JUST WHAT THEY WANT OR DO YOU GO FURTHER TO GIVE THEM WHAT THEY NEED (THE WORD OF GOD) WHICH WILL SOLVE THEIR PROBLEMS AND MEET THEM AT THE POINT OF THEIR NEEDS. LET US PREACH THE WORD OF GOD TODAY. JESUS CHRIST IS COMING VERY SOON. VS 3 THEY BROUGHT UNTO HIM ONE SICK OF THE PALSY. THIS MAN COULD NOT HELP HIMSELF. HE HAD TO BE CARRIED BY OTHERS TO JESUS CHRIST. HIS FRIENDS HAD FAITH AND JESUS SAW THEIR FAITH AND FORGAVE HIS SINS. CHRISTIANS SHOULD PREACH THE WORD AND TAKE PEOPLE TO JESUS CHRIST SO THAT THEY MAY BE FORGIVEN AND SAVED. JESUS KNEW THE FUNDAMENTAL SOURCE OF THE PROBLEM AND KNEW WHAT TO DO TO HAVE AN EVERLASTING SOLUTION. VS 4 WHEN THEY COULD NOT COME NIGH UNTO HIM FOR THE PRESS, THEY UNCOVERED THE ROOF, BROKE IT UP AND LET DOWN THE BED WHEREIN THE SICK OF THE PALSY LAY. THERE WAS NO DOUBT THAT THE FOUR MEN WERE REALLY DETERMINED TO GET THEIR FRIEND TO JESUS CHRIST. WHAT KIND OF FRIEND ARE YOU? ARE YOU DETERMINED TO GET YOUR FRIENDS, FAMILY AND NATION TO JESUS CHRIST? PLEASE START TODAY. THAT IS THE GREAT COMMISSION. WHAT A FRIEND THEY WERE? WHAT FAITH THEY HAD? THIS IS WHAT IS EXPECTED OF EVERY CHRISTIANWE MUST BE DETERMINED WHEN IT COMES TO SPREADING THE GOOD NEWS. WE MUST SHOW COMPASSION WE MUST LOVE THE SINNER BUT HATE SIN. NOTICE THAT WHEN THEY BROUGHT THE MAN TO JESUS CHRIST, THEY LET GO AND LET JESUS CHRIST DO THE REST. WE HAVE TO LET GO OF OUR PROBLEMS AT THE FEET OF JESUS CHRIST. WE MUST DECIDE TO FOLLOW JESUS CHRIST. WE MUST COME TO JESUS CHRIST BY CHOICE NOT BY CHANCE . WE MUST TAKE ALL OUR PROBLEMS TO JESUS CHRIST AND LEAVE THEM WITH HIM. HE KNOWS HOW TO HANDLE THEM. VS 5 JESUS CHRIST SAW THEIR FAITH. WHAT DOES JESUS CHRIST SEE IN YOU? DOES HE SEE YOUR FAITH? THEN HE SAID TO THE SICK OF THE PALSY, SON THY SINS BE FORGIVEN THEE. THIS IS IMPORTANT. JESUS CHRIST HAS POWER TO FORGIVE SINS. WHEN YOU ARE FORGIVEN, YOU ARE MADE WHOLE. THE MAN WAS CARRIED IN HIS BED TO JESUS CHRIST. WHEN JESUS CHRIST FORGAVE HIM HIS SINS, HE CARRIED HIS BED HOME. JESUS CHRIST CAME TO SAVE US FROM OUR SINS. LET US ACCEPT JESUS CHRIST TODAY SO THAT WE MAY BE SAVED. JESUS CHRIST IS COMING SOON. THANK YOU AND GOD BLESS YOU.

SOME ANALYTICAL TOOLS

VECTORS AND VECTOR ANALYSIS A DIRECTED LINE SEGMENT IS CALLED A VECTOR. THE LENGTH IS CALLED THE LENGTH OF THE VECTOR. AND THE DIRECTION IS CALLED THE DIRECTION OF THE VECTOR. TWO VECTORS ARE EQUAL IF AND ONLY IF THEY HAVE THE SAME LENGTH AND THE SAME DIRECTION. THE LENGTH OF A VECTOR IS CALLED THE EUCLIDEAN NORM OR MAGNITUDE. INNER PRODUCT(DOT PRODUCT) THIS IS ALSO CALLED SCALAR PRODUCT THE RESULT IS A SCALAR a.b = |a||b|cosϒ for a=/= 0, b=/= 0 a.b = 0 a=0 or b=0 and ϒ(0<ϒ<π) IS ANGLE B/W a&b THIS IS COMPUTED WHEN THE VECTORS HAVE THEIR INITIAL POINT COINCIDING. VECTOR PRODUCT ( CROSS PRODUCT) THE RESULT IS A VECTOR Axb (or a^b) v = axb = 0 THIS IS THE CASE IF AND ONLY IF THE VECTORS a AND b HAVE THE SAME OR OPPOSITE DIRECTION OR ONE OF THESE VECTORS IS THE ZERO VECTOR. IN ANY OTHER CASE, v = axb LENGTH = AREA OF PARALLELOGRAM WHOSE SIDES ARE a & b. DIRECTION = PERPENDICULAR TO BOTH a AND b a,b,v FORM A RIGHT HANDED TRIPLE OR RIGHT HANDED TRIAD |v|=|a||b|sinϒ

A BIBLE STUDY ON FORGIVENESS

2 Corinthians chapter 2 King James Version 1 But I determined this with myself, that I would not come again to you in heaviness. 2 For if I make you sorry, who is he then that maketh me glad, but the same which is made sorry by me? 3 And I wrote this same unto you, lest, when I came, I should have sorrow from them of whom I ought to rejoice; having confidence in you all, that my joy is the joy of you all. 4 For out of much affliction and anguish of heart I wrote unto you with many tears; not that ye should be grieved, but that ye might know the love which I have more abundantly unto you. 5 But if any have caused grief, he hath not grieved me, but in part: that I may not overcharge you all. 6 Sufficient to such a man is this punishment, which was inflicted of many. 7 So that contrariwise ye ought rather to forgive him, and comfort him, lest perhaps such a one should be swallowed up with overmuch sorrow. 8 Wherefore I beseech you that ye would confirm your love toward him. 9 For to this end also did I write, that I might know the proof of you, whether ye be obedient in all things. 10 To whom ye forgive any thing, I forgive also: for if I forgave any thing, to whom I forgave it, for your sakes forgave I it in the person of Christ; 11 Lest Satan should get an advantage of us: for we are not ignorant of his devices. 12 Furthermore, when I came to Troas to preach Christ's gospel, and a door was opened unto me of the Lord, 13 I had no rest in my spirit, because I found not Titus my brother: but taking my leave of them, I went from thence into Macedonia. 14 Now thanks be unto God, which always causeth us to triumph in Christ, and maketh manifest the savour of his knowledge by us in every place. 15 For we are unto God a sweet savour of Christ, in them that are saved, and in them that perish: 16 To the one we are the savour of death unto death; and to the other the savour of life unto life. And who is sufficient for these things? 17 For we are not as many, which corrupt the word of God: but as of sincerity, but as of God, in the sight of God speak we in Christ. LET US TAKE A LOOK AT THIS PASSAGE IN SOME CONSIDERABLE DETAIL Vs 4 Love made manifest in the nature of the writing. Only sincere love will correct sincerely. Vs 7 Ye ought rather to forgive him, and comfort him lest perhaps such a one should be swallowed up with much sorrow. Vs 8 When you forgive you confirm your love toward him Vs 9 This is also a prove of obedience. Vs 10 Everybody must forgive. Vs 11 When you forgive you will not fall into the trap of sin. Vs 12 The Lord opens doors Vs 14 Thank God who causes us to triumph in Christ and maketh manifest the savour of His knowledge by us in every place Vs 15 We are unto God a sweet savour of Christ, in them that are saved and in them that perish. Vs 16 To the one we are the savour of death unto death And to the other the savour of life unto life. And who is sufficient for these things Vs 17 For we are not as many which corrupt the word of God, But as of sincerity but as of God in the sight of God speak we in Christ.

FORGIVENESS

FORGIVENESS TEXT : MARK 2 2CORINTHIANS 2 YOU FORGIVE, NOT BECAUSE YOU WANT TO NOR BECAUSE YOU LIKE TO NOR BECAUSE YOU CAN BUT BECAUSE THE SPIRIT OF GOD IN YOU FORGIVES THROUGH YOU. WHEN YOU FORGIVE, YOU INCEASE YOUR FORGIVENESS ACCOUNT WITH GOD IN HEAVEN. AS YOU FORGIVE SO ALSO ARE YOU FORGIVEN. YOU HAVE TREASURES IN HEAVEN WHEN YOU FORGIVE ON EARTH. FORGIVENESS OPENS A NEW CHAPTER FOR YOU IN LIFE. FORGIVENESS GIVES YOU THE OPPORTUNITY FOR A NEW BEGINNING. FORGIVENESS MAKES YOU TO MOVE FORWARD IN LIFE. FORGIVENESS ENSURES THAT YOU DO NOT WORRY ABOUT THE PAST. FORGIVENESS ENSURES THAT YOU DO NOT DWELL OR LIVE IN THE PAST. FORGIVENESS IS OF GOD. JESUS CHRIST DID NOT PROMISE US AN EASY LIFE. JESUS CHRIST PROMISED US A VICTORIOUS LIFE. JESUS CHRIST PROMISED US A SUCCESSFUL LIFE. THE SUCCESS OF GOD IS GODLY, SUSTAINABLE, GOOD SUCCESS. THE WISDOM OF GOD GOOD AND GODLY AND IS OF GOD AND IS FROM ABOVE AND IS ABOVE ALL FOR GOD IS GOD AND GOD IS ABOVE ALL THINGS. FORGIVENESS BRINGS HEALING. YOU MUST FORGIVE BECAUSE YOU ARE FORGIVEN. GOD HAS FORGIVEN US ALL. LET US ACCEPT THE FORGIVENESS OF GOD AND FORGIVE OTHERS ALSO. THE ABILITY TO FORGIVE COMES FROM GOD. WHEN YOU ARE FORGIVEN, FORGIVE YOU ARE SAVED AND HEALED AND YOUFORGIVE ALSO. WHEN YOU ARE NOT ABLE TO FORGIVE OTHERS, ASK YOURSELF, WHY? WHEN YOU DO NOT FORGIVE FIND OUT WHY. WHEN YOU ARE NOT FORGIVING LOOK INWARDS. GOD MAKES IT POSSIBLE FOR YOU TO FORGIVE. IT TAKES THE POWER AND SPIRIT OF GOD TO FORGIVE. THE CHILDREN OF GOD FORGIVE. YOU MUST FORGIVE. WHEN YOU BELIEVE IN OUR LORD JESUS CHRIST, HE GIVES YOU THE POWER TO BECOME A CHILD OF GOD. IT IS THIS HOLY SPIRIT OF GOD IN YOU THROUGH OUR FAITH AND BELIEVE IN OUR LORD JESUS CHRIST THAT FORGIVES. BELIEVE IN OUR LORD JESUS CHRIST TODAY LET US LOVE ONE ANOTHER. LET US LOVE OUR ENEMIES. LET US FORGIVE ONE ANOTHER. LET US FORGIVE OUR ENEMIES. THANK YOU AND GOD BLESS YOU.

MORE INTERESTING STATISTICS

STATISTICS IS IMPORTANT IN EVERY DAY LIFE. IT ENABLES US TO ANALYSE DATA AND TO PRESENT DATA FOR VARIOUS PURPOSES. CONSIDER THE FOLLOWING STATISTICAL DATA.

STATISTICS IS IMPORTANT IN EVERY DAY LIFE. IT ENABLES US TO ANALYSE DATA AND TO PRESENT DATA FOR VARIOUS PURPOSES. CONSIDER THE FOLLOWING STATISTICAL DATA.

INTERESTING STATISTICS

STATISTICS IS IMPORTANT IN EVERY DAY LIFE. IT ENABLES US TO ANALYSE DATA AND TO PRESENT DATA FOR VARIOUS PURPOSES. CONSIDER THE FOLLOWING STATISTICAL DATA.

A REVIEW OF ADDITIONAL STATISTICS

STATISTICS IS IMPORTANT IN EVERY DAY LIFE. IT ENABLES US TO ANALYSE DATA AND TO PRESENT DATA FOR VARIOUS PURPOSES. CONSIDER THE FOLLOWING STATISTICAL DATA.

ADDITIONAL STATISTICS

STATISTICS IS IMPORTANT IN EVERY DAY LIFE. IT ENABLES US TO ANALYSE DATA AND TO PRESENT DATA FOR VARIOUS PURPOSES. CONSIDER THE FOLLOWING STATISTICAL DATA.

ADDITIONAL STATISTICS

STATISTICS IS IMPORTANT IN EVERY DAY LIFE. IT ENABLES US TO ANALYSE DATE AND TO PRESENT DATA FOR VARIOUS PURPOSES. CONSIDER THE FOLLOWING STATISTICAL DATA.