Question

Find the magnitude of the electric field $\left(|\overrightarrow{E_{ind}}|\right)$ at the center of the sphere due to the induced charges on the sphere.

• A. $\frac{Kq}{2}$
• B. $\frac{Kq}{8}$
• C. $\frac{Kq}{5}$
• D. $\frac{Kq}{4}$

Answer 1

The correct option is D $\frac{Kq}{4}$

We know that, net electric field inside a conductor is zero
i.e. $(\overrightarrow{E_{net}}{)}_{@O}=0$

Since the net electric field at the center is the sum of the electric fields due to charge $q$ and due to the induced charge on the sphere,

$\overrightarrow{E_{net}}=\overrightarrow{E_q}+\overrightarrow{E_{ind}}=0$

$\Rightarrow \overrightarrow{E_{ind}}=-\overrightarrow{E_q}$

$\therefore |\overrightarrow{E_{ind}}|=\frac{Kq}{(2{)}^2}=\frac{Kq}{4}$

Hence, option (d) is the correct answer.