Q. The electric field and electric potential at a point are E avd V respectively.

(a). If E=0, V must be 0

(b). If V=0, E must be zero.

(c). If E is not equal to 0, V cannot be 0

(d). If V is not equal to 0, E cannot be 0.

if potential is zero then electric field must be  zero option B,D  are correct  if electric field is zero then field must not be zero option A is not correct.

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Perhaps Option (b) is correct.

As:

E = -dV/dr

If V is Zero, E = 0/

But if E = 0, V = constant, not necessarily zero.

Use the knowledge of Electric field and  Potential in dipole.Electric field and equatorial point is kp/r³  where r>>a. But V at eqatorial point is 0.

I can give you examples to disprove the wrong answers.

a)Take four charges q at four corners of a square.E=0, V is non zero.

b)Consider two collinear point charges seperated by 2d. Potential at the center of the line joining the charges is zero, But E is not zero.

c)Consider the same above case(b), E isn''t equal to zero but V=0.

d)Same as the first case, V isn''t zero but E is zero.

Therefore none are correct!!

Prajwal

b is correct bcaze E=dv/dt so if v=0 so E is also=0

(a)