Question

A hollow metallic sphere of radius $10cm$ is given a charge of $3.2x{10}^{-9}C$. The electric intensity at a point $4cm$ from the center is

• A. $9x{10}^{-9}N{C}^{-1}$
• B. $288N{C}^{-1}$
• C. $2.88N{C}^{-1}$
• D. Zero

Answer 1

The correct option is D

Zero

Step 1. Given data:

1. Radius of the sphere $10cm$
2. Given a charge $3.2x{10}^{-9}C$
   

Step 2. Formula used:
According to Gauss’ law,

$\oint E.ds=\frac{q_{in}}{{\epsilon }_0}$

Where,

$E$ is the electric field intensity at a distance $r$from the center of the surface of radius $R$

$q_{in}$ is the charge inside the Gaussian surface.

${\epsilon }_0$ is the permittivity

Step 3. Calculating electric field.

It is given that in the sphere charge is evenly distributed on the surface. So there is no charge inside the hollow sphere.

So $q_{in}$ is zero

$\therefore \oint E.ds=\frac{0}{{\epsilon }_0}=0$

Since the electric field is constant, we get

$$\begin{gathered} \Rightarrow \oint E.ds=0 \\ \Rightarrow E\oint ds=0 \end{gathered}$$

$\Rightarrow E\left(4\pi r^2\right)=0$ [$\because$Surface area of the sphere of radius $r$ is $4\pi r^2$]

$\Rightarrow E=0$

So, at any point inside the hollow sphere electric field is zero.

Hence, Option D is correct.