Question

We have an isolated conducting spherical shell of radius $10cm$. Some positive charge is given to it so that the resulting electric field has a maximum intensity of $1.8\times {10}^{6}N{C}^{-1}$.The same amount of negative charge is given to another isolated conducting spherical shell of radius $20cm$. Now, the first shell is placed inside the second so that both are concentric as shown in figure. The electrostatic energy stored in the system is :

• A. $1.0J$
• B. $0.045J$
• C. $0.09J$
• D. $1.8J$

Answer 1

The correct option is C $0.09J$

Let the charge on the shell of 10 cm radius is $Q$.
$E=\frac{Q}{4\pi {ϵ}_0(0.1{)}^2}\Rightarrow Q=1.8\times {10}^6\times 4\pi {ϵ}_0(0.1{)}^2$

When $10cm$ radii shell is kept inside $20cm$ radii shell the whole charge $Q$ will appear on the surface of outer shell.

The electric field intensity just inside the outer sphere is: $E^{\prime }=\frac{Q}{4\pi {ϵ}_0(0.2{)}^2}=\frac{1.8\times {10}^6\times (0.1{)}^2}{{0.2}^2}=4.5\times {10}^{5}N{C}^{-1}$

As the energy is stored over the surface of shell of radii 20 cm so its stored energy is:
$W=\frac{{ϵ}_0}{2}{E}^{\prime 2}.4\pi (0.2{)}^2=\frac{8.85\times {10}^{-12}}{2}\times {4.5}^2\times {10}^{10}\times 4\pi (0.2{)}^2=0.09J$