ELECTRIC POTENTIAL DIFFERENCE (V) & ELECTRIC POTENTIAL ENERGY (U)

ELECTRIC POTENTIAL (V) & ELECTRIC POTENTIAL ENERGY(U):-

V_A=Potential of plate A

V_B=Potential of plate B

U_A=Potential Energy of plate A

U_B=Potential Energy of plate A

∆V=Potential Difference between the plates=      V_B-V_A

∆U=Electric Potential Energy difference of plates=U_B-U_A

If we place any charge +q inside this field then charge will accelerate from positive plate to negative plate in direction of electric field. However if we , with an external force, move the charge from negative to positive plate then external work have to be done this work appear as electric potential energy of  the charge while keeping the charge under electrostatic equilibrium ( that is charge move with constant velocity). Electric potential difference is defined as the amount of work done in moving the charge between two plates 

i.e Electric potential difference= Work done in moving the charge from plate A to B  -----(i)

                                                                       magnitude of charge

∆V= W_A→B

Electric potential difference can also be defined as the ratio between the electric potential energy and charge  according to eq (iv) also

∆U=q x ∆V----(vi)

whereas electric potential energy is equal to product of potential difference and charge according to (vi).If plate A is taken away at infinite distance with respect to plate B then ∆V_A= 0 and (iii) & (v) can be written as 

Whenever charge is moves with in electric field between two points then we use the term electric potential energy. However if charge is moved to infinity and is brought inside the electric field then the work done is called absolute potential energy.Both potential energy and potential difference are scalar quantities.The difference between them is that Electric potential energy results from forces between charges; potential difference is the energy needed to move a charge from point A to B.