Question

A spherical shell of radius $R=1.5cm$ has a charge $q=20\mu C$ uniformly distributed over it. The force exerted by one half over the other half is

• A. Zero
• B. ${10}^{-2}N$
• C. $500N$
• D. $2000N$

Answer 1

Answer: (D)

$2000N$

$\varphi =\overrightarrow{E}\cdot \overrightarrow{A}=300units$

$E=\frac{\sigma }{2{ϵ}_0}$

$F=Edr=\frac{\sigma dA\sigma }{2{ϵ}_0}$

$P=\frac{F}{dA}=\frac{{\sigma }^2}{2{ϵ}_0}$

$Force=P\pi R^2=\frac{{\sigma }^2}{2{ϵ}_0}\pi R^2$

$=\frac{Q^2}{16{\pi }^2{R}^4}\frac{\pi R^2}{2{ϵ}_0}=\frac{Q^2}{32\pi {ϵ}_0{R}^2}$

$=\frac{(20\times {10}^{-6}{)}^2\times 9\times {10}^9}{8(1.5\times {10}^{-2}{)}^2}=2000N$.