ELECTRIC FIELD AS POTENTIAL GRADIENT

ELECTRIC FIELD AS POTENTIAL GRADIENT:-

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

this shows that potential gradient is rate of change of potential with respect to displacement

from (v) unit of E is V/m but we also know that E has unit N/C actually both are same if we simplify them.