Gravitational Potential due to Spherical Shell of Matter

Suppose P is a particle having unit mass, outside the spherical shell of radius r. Let, A = distance between the particle P and the centre of the spherical shell = OP. \(\sigma\) = surface density of the material of the spherical shell. Let us cut the spherical shell at the planes LM and KL perpendicular to OP & close to each other to get the slice KLMN. Let LP = x, \(\angle\)LOP = Q & \(\angle\)KOL = dQ. \(\therefore\) The width of the slice = KL = r.dQ In the \(\triangle\) LQO, LQ = r\(sin\phi\) \(\therefore\) The length of the slice = 2\(\pi\)π‘Ÿ\(sin\theta\) \(\therefore\) The surface area of the slice = 2\(\pi\)π‘Ÿ\(sin\theta\) . π‘Ÿπ‘‘π‘„ = 2\(\pi\)\(π‘Ÿ^2\) \(sin\theta\) . 𝑑𝑄 \(\therefore\) The mass of the slice = 2\(\pi\)\(π‘Ÿ^2\)\(sin\theta\). 𝑑𝑄. \(\sigma\) = 2\(\pi\)\(\sigma\)\(π‘Ÿ^2\)\(sin\theta\) . \(d\theta\) (Here, the thickness of the slice or spherical shell has been neglected). As the particle P is at the same distance from every mass element of the slice, the gravitational potential

To continue reading "Gravitational Potential due to Spherical Shell of Matter", login now.

This page has been protected for subscriber only.