Question

Find the energy stored in the shaded region. If $11\mu C$ charge is placed at centre.

• A. $2.2J$
• B. $1.1J$
• C. $4.4J$
• D. $3.3J$

Answer 1

Answer: (D)

We know, the energy stored by a charge outside the sphere of radius $R$ in medium of relative permittivity, ${ϵ}_r=2.2$, is given by,

$E=\frac{1}{2}\frac{k{Q}^2}{{ϵ}_{r}R}$

We need to find energy stored over a region of shaded area

Let $a=3cm$ and $b=5cm$

$Q_{1}1\mu C=11\times {10}^{-6}C$

${ϵ}_r=2.2$

$k=9\times {10}^{9}units$

Required energy is given by,

$E_{req}=\frac{1}{2}\frac{k{Q}^2}{{ϵ}_{r}a}-\frac{1}{2}\frac{k{Q}^2}{{ϵ}_{r}b}$

$=\frac{1}{2}\frac{k{Q}^2}{{ϵ}_r}[\frac{1}{a}-\frac{1}{b}]$

$=\frac{1}{2}\frac{9\times {10}^9(11\times {10}^{-6}{)}^2}{2.2}[\frac{1}{3\times {10}^{-2}}-\frac{1}{5\times {10}^{-2}}]$

$=\frac{9\times {11}^2\times 2\times {10}^{-2}}{2\times 2.2\times 15}=3.3J$