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.