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Principle of Superposition

A spherical c...

Question

A spherical cavity of radius $r$ is made in a conducting sphere of radius $2 r$ . A charge $q$ is kept at the centre of cavity as shown in the figure. The magnitude of the total electric field at $(4 r, 0, 0)$ is $\frac{K q}{P r^{2}}$ . The value of P is (Answer upto two decimal places.)

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Solution

The charges gets distributed as shown in the figure. The field due to the charges inside the sphere is zero. So, the field due to the charges on the external surface is simply,
$E = \frac{K q}{(4 r)^{2}} = \frac{K q}{16 r^{2}}$

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