A thin spherical shell having uniform density is cut into two parts by a plane and kept separated. P

Question

A thin spherical shell having uniform density is cut into two parts by a plane and kept separated. Point A is the centre of the plane section of the first part and B is the centre of the plane section of the second part. Let the magnitude of the gravitational field at A due to the first part be $E_A$ and the field at B due to the second part be $E_B$. Which of the following relations is correct?

Professor PC Thomas Classes · Answer

When the two parts are perfectly joined to reconstruct the complete spherical shell, points A and B coincide at a single location inside the shell. According to the shell theorem, the net gravitational field anywhere inside a uniform spherical shell is strictly zero. Thus, the vector sum $\vec{E}_A + \vec{E}_B = 0$, which implies $\vec{E}_A = -\vec{E}_B$. Therefore, their magnitudes are exactly equal, meaning $E_A = E_B$.