Question

The radius of a conducting spherical shell is 10 mm, and a $ 100\mu C $ charge is spread on it. The force acting on a $ 10\mu C $ charge placed at its centre is:

Answer 1

Hint : Since only one radius is given to us, this implies that we are to assume a thin spherical shell. For any hollow object with no charge within the object but only on the surface, the electric field anywhere inside is non-existent.

Formula used: In this solution we will be using the following formulae; $ F = qE $ where $ F $ is the force exerted on a charge due to an electric field, $ q $ is the value of the charge and $ E $ is the electric field at the location of the charge.

Complete step by step answer
In our question, we are informed that a conducting spherical shell has a radius of 10 mm, and a charge of $ 100\mu C $ is distributed on the surface. We are to find the force acting on a $ 10\mu C $ which is placed at the centre of the shell.
The problem can easily be solved if we assume that the shell is thin (negligible with relative to radius). It is safe to assume so since only one value of radius is given.
Now, generally, without the presence of the charge, the electric field inside any hollow object is zero.
Hence, the electric field is zero, hence from the equation
 $ F = qE $ where $ F $ is the force exerted on a charge due to an electric field, $ q $ is the value of the charge and $ E $ is the electric field at the location of the charge, we see that the force on the charge would be equal to zero, as in
 $ F = 10(0) = 0N $ .

Note
However, for clarity for thick shells, although without the presence of a charge, the electric field is still zero, but with the presence of the charge there may be a significant induction whereby the negative charges (electrons) on the shell migrate to the inner surface leaving behind a positive charge on the outer surface. This difference in radius creates a difference in their electric field inside the shell.