Question

Consider two points $1$ and $2$ in a region outside a charged sphere. Two points are not vary far away from the sphere. If $E$ and $V$ represent the electric field vector and the electric potential, which of the following is not possible?

• A. $|\overrightarrow{E_1}|=|\overrightarrow{E_2}|,V_1=V_2$
• B. $|\overrightarrow{E_1}|\ne |\overrightarrow{E_2}|,V_1\ne V_2$
• C. $|\overrightarrow{E_1}|\ne |\overrightarrow{E_2}|,V_1=V_2$
• D. $|\overrightarrow{E_1}|=|\overrightarrow{E_2}|,V_1\ne V_2$

Answer 1

The correct option is D $|\overrightarrow{E_1}|=|\overrightarrow{E_2}|,V_1\ne V_2$

If electric fields at two points outside the charged sphere, (for equal distances from the centre) are same then both points must be equipotential points.

Thus, if $\left|{\overrightarrow{E}}_1\right|=\left|{\overrightarrow{E}}_2\right|$, $V_1\ne V_2$, then it is not possible.