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The electric field and the electric potential at a point are $E$ and $V$ respectively.

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If $E \neq 0$ , $V$ may be zero

If $E = 0$ , $V$ may be zero

If $V \neq 0$ , $E$ may be zero.

If $V = 0$ , $E$ may be zero

answer is A, B, C, D.

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Detailed Solution

E = - $\frac{d V}{d r}$

If $E = 0$ then $\frac{d V}{d r} m u s t b e z e r o a n d i n t h i s c a s e V m a y b e z e r o .$

If V and $\frac{d V}{d r} b o t h a r e z e r o, t h e n E i s z e r o .$

At the equator of the dipole $E \neq 0$ , but $V = 0$ .

Inside conductor, $E = 0$ , $V \neq 0$

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