Question

relation between electric field and potential

Answer 1

As you know, standard formula of electric field intensity and potential are given by 

E = KQ/r² , V = KQ/r , here Q is the charge , r is the distance between charge and observation point . 


V = KQ/r

differentiate with respect to r 

dV/dr = -KQ/r² = -E 

dV = -E.dr or, E = -dV/dr 

Hence, relation between Electric field intensity and potential is E = -∆V/∆r 

Answer 2

Hence electric field is negative gradient of the scalar potential. The negative sign came as a result because the difference is the work done per unit charges against the electrostatic force to move a charge from a to b. However, this equation is valid only for electrostatic fields.
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