A spherical shell is cut into two pieces alon | vedclass

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(C) The gravitational field inside a uniform spherical shell is zero at every point.Let $I_1$ be the gravitational field at point $P$ due to the upper

Vedclass · Accepted Answer

$I_1 = I_2$

Vedclass · Answer

(C) The gravitational field inside a uniform spherical shell is zero at every point.Let $I_1$ be the gravitational field at point $P$ due to the upper part of the shell and $I_2$ be the gravitational field at point $P$ due to the lower part of the shell.The total gravitational field at point $P$ due to the entire shell is the vector sum of the fields due to its parts: $\vec{I}_{total} = \vec{I}_1 + \vec{I}_2 = 0$.Since the point $P$ lies on the plane of the cut,the field vectors $\vec{I}_1$ and $\vec{I}_2$ must be equal in magnitude and opposite in direction to satisfy the condition $\vec{I}_1 + \vec{I}_2 = 0$.Therefore,the magnitudes of the gravitational fields are equal: $I_1 = I_2$.

$A$ spherical shell is cut into two pieces along a plane as shown in the figure. $P$ is a point on the plane of the cut. The gravitational field at $P$ due to the upper part is $I_1$ and that due to the lower part is $I_2$. What is the relation between them?

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