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