Question

A metallic sphere of radius 18 cm has been given a charge of $5\times {10}^{-6}$ C. The energy of the charged conductor is:

• A. $0.2J$
• B. $0.6J$
• C. $1.2J$
• D. $2.4J$

Answer 1

The correct option is B $0.6J$

$R=18cm=0.18m$

$C=\frac{4{ϵ}_0\pi }{(\frac{1}{a}-\frac{1}{b})}=\frac{4\pi {ϵ}_0}{4R}=4R{ϵ}_{0}R[a=R,b=\infty ]Q=CVV=\frac{Q}{C}$

$Energy=\frac{1}{2}C{V}^2=\frac{1}{2}\left(4\pi {ϵ}_{0}R\right)(\frac{Q}{C}{)}^2=\frac{Q^2}{2C}=\frac{(5\times {10}^{-6}{)}^2}{2\times 4\pi {ϵ}_{0}R}=\frac{25\times {10}^{-12}}{2\times 4\times 3.14\times 8.5\times {10}^{-12}\times 0.18}=0.62\approx 0.6J$