Question

A charge q is placed in front of a neutral metallic sphere. The magnitude of electric field at the centre of sphere due to the induced charge on the surface of sphere is

• A. $E = \frac {1}{4 \pi \epsilon_o} \frac {q}{R^2}$
• B. $E = \frac {1}{4 \pi \epsilon_o} \frac {q}{R}$
• C. $E = \frac {1}{4 \pi \epsilon_o} \frac {q}{d^2}$
• D. $Zero$

Answer 1

Answer: (C)

Net electric field inside metal is zero.
$\overrightarrow{E}_{sphere}+\vec{E_{q}}=0$
$\overrightarrow{E}_{sphere}= -\vec{E_{q}}=\frac{1}{4\pi\varepsilon_{o}}\frac{q}{d^{2}}$
$\left|\overrightarrow{E}_{sphere}\right|=\frac{1}{4\pi\varepsilon_{o}}\frac{q}{d^{2}}$