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In a region of space, the gravitational field intensity is given by E = -k/r, where r is the distance from the origin and k is a positive constant. Given that the gravitational potential at r = r0 is V0, derive an expression for the gravitational potential V at an arbitrary distance r.
- k * loge(r/r0)
- k * loge(r0/r)
- V0 + k * loge(r/r0)
- V0 + k * loge(r0/r)
Correct answer: V0 + k * loge(r/r0)
Solution
Integrating dV/dr = k/r yields V = k*ln(r) + C. Applying V(r0) = V0 gives C = V0 - k*ln(r0), so V = V0 + k*ln(r/r0).
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