Question

Show that at a point where the electric field intensity is zero, electric potential need not be zero.

Answer 1

one case which comes to my mind .. is case of hollow conducting sphere. there is no electric feild inside but there is potential inside the conductor.

Answer 2

Use the Relation $E = -\frac {dV}{dr}$

Step-by-step explanation:

• From relation between Electric field strength and potential, We know that

$E = -\frac {dV}{dr}$

• Thus if we are considering the field to be zero then above relation becomes

$\frac {dV}{dr} = 0$

V = constant

• Therefore a derivative value when $\frac {dV}{dr} = 0$  means that there is no change the dependent value with respect to other independent value.

Therefore according to above relation we get V as constant value.

• Inside a charge conductor electric field is zero but potential remains constant.