Q: The gravitational field due to a mass distribution is given by E = – K/x^{3} in X- direction. Taking the gravitational potential to be zero at infinity, find its value at a distance x.

Sol: The potential at a distance x is

$\large V = -\int E dx$

$\large V = \int_{\infty}^{x} \frac{K}{x^3} dx$

$\large V = [-\frac{K}{2x^2}]_{\infty}^{x} $

$\large V = \frac{-K}{2 x^2} $