Let V and E denote the gravitational potential and gravitational field at a point. It is possible to have
A. V = 0 and E = 0
B. V = 0 and E ≠ 0
C. V ≠ 0 and E = 0
D. V ≠ 0 and E ≠ 0
Let us consider a spherical shell of some mass and radius R as given in the figure below. At point A, we have V = 0 and E = 0 as the object is at infinity.
At D, we have the object at a certain distance r>R. So here, V ≠ 0 and E ≠ 0.
At point C inside the shell, V ≠ 0 and E = 0.
For B to be true, the potential has to be a linear function of distance r. For example, let .
The electric field at is . While the potential at is .
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