Question

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

• A. $\frac{KQ}{5}$
• B. $\frac{KQ}{25}$
• C. $\frac{KQ}{16}$
• D. $\frac{KQ}{4}$

Answer 1

The correct option is B $\frac{KQ}{25}$


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

Since the net electric field at point $\text{A}$ is the sum of the electric fields due to charge $Q$ and due to the induced charge on the sphere,

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

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

$\therefore |\overrightarrow{E_{ind}}|=\frac{KQ}{(5{)}^2}=\frac{KQ}{25}$

Hence, option (b) is the correct answer.

Why this question? This question checks the basic understanding of the electric field inside a conductor and the concept of induced charges.