Question

A solid conducting sphere having charge $4\mu C$ is placed on non-conducting stand. A point charge $2\mu C$ is placed at a distance from the centre of the sphere, at a double distance of radius of the sphere as shown in the figure. If conducting sphere is earthed then charge flow into the ground is :

• A. $5\mu C$
• B. $2\mu C$
• C. $10\mu C$
• D. $1\mu C$

Answer 1

The correct option is A $5\mu C$

Let $x$ charge flows into ground
Now charge on sphere=$(4-x)\mu C$
As the charge distribution will not be uniform on surface of sphere due to unsymmetrical distribution of charge on sphere, for calculating the potential at surface, the potential at center can be calculated as the distance of charge from sphere is constant $R$, and this potential will be equal inside the sphere everywhere.
Conducting sphere is connected to ground , therefore net potential of sphere should be zero
$\frac{K(4-x)}{R}+\frac{2K}{2R}=0$
$2x=10$ $\Rightarrow x=5$