Question

In a conducting hollow sphere of inner and outer radii $5\text{cm}$ and $10\text{cm}$, respectively, a point charge $1\text{C}$ is placed at point $A$, that is $3\text{cm}$ from the center $C$ of the hollow sphere. An external uniform electric field of magnitude $20\text{N/C}$ is also applied. Net electric force on this charge is $15\text{N}$, away from the center of the sphere as shown in the figure. Find the magnitude of net force exerted on the charge placed at point $A$ by the induced charges on the sphere.

• A. $15\text{N}$
• B. $20\text{N}$
• C. $25\text{N}$
• D. $35\text{N}$

Answer 1

The correct option is D $35\text{N}$

Given,

Applied electric field $E=20\text{N/C}$

Net electric force on the charge placed at point $A$ , $F=15\text{N}$

Inner radius of hollow sphere $r_1=5\text{cm}$

Outer radius of hollow sphere $r_2=10\text{cm}$

We know that net electric field intensity inside the conducting region is zero.

Thus, external electric field is neutralised by charge induced on outer surface.

Implies, force supplied by the induced charges present on outer surface should be equal and opposite to that applied by electric field.

$\Rightarrow F=qE=1\times 20=20\text{N}$ (towards left)

Given that, $15\text{N}$ force is acting due to induced charge on inner surface of hollow sphere.

Thus, net force by induced charges will be $20+15=35\text{N}$

Hence, option (d) is the correct answer.