The electric field and the electric potential at a point are E and V respectively.
A. If E = 0, V must be zero.
B. If V = 0, E must be zero.
C. If E ≠ 0, V cannot be zero
D. If V ≠ 0, E cannot be zero.
We know that electric field is negative of the space rate of change of electric potential in a region. i.e.
Option (a) is incorrect as for E =0, V=0 is not the only condition. As we can see from the above equation, electric field is the negative of vector derivative of V that means
if V=constant, then also, E=0.
Option (b) is incorrect as:
If at a point, the electric potential is zero, it doesn’t imply electric field to be also zero.
Take an example of a dipole where somewhere between the two charges on its axial line, there exists a point where potential is zero but electric field is always non zero and directs in the direction from positive charge to negative charge.
Option (c) is incorrect as if E≠0, it doesn’t mandate the potential to be non-zero. We can take again the example of a dipole where somewhere at a point on its axial line, there exists a point where E≠0 but V=0. So the statement “If E ≠ 0, V cannot be zero” is incorrect.
Option (d) is incorrect as:
If V ≠ 0 (let’s say V= non-zero constant)
Which is contradicted in the given statement.
Thus, none of the options is correct.
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