Question 742: Electrostats & Capacitance

Question

The volume charge density of a sphere of radius $$6 \mathrm{~m}$$ is $$2 \,\mu \mathrm{C} \,\mathrm{cm}^{-3}$$. The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ $$	imes 10^{10} \,\mathrm{NC}^{-1}$$.
[Given : Permittivity of vacuum $$\epsilon_{0}=8.85 	imes 10^{-12} \,\mathrm{C}^{2}\, \mathrm{~N}^{-1}-\mathrm{m}^{-2}$$ )

Accepted Answer

$$ho$$ = 2 $$\mu$$c/cm
3
R = 6 m
Number of lines of force per unit area = Electric field at surface.
$$ = {{KQ} \over {{R^2}}}$$
$$ = {1 \over {4\pi {\varepsilon _0}}}{{ho {4 \over 3}\pi {R^3}} \over {{R^2}}}$$
$$ = {{ho R} \over {3{ \in _0}}}$$
$$ = {{2 	imes {{10}^{ - 6}} 	imes {{10}^6} 	imes 6} \over {3 	imes 8.85 	imes {{10}^{ - 12}}}}$$
$$ = 0.45197 	imes {10^{12}}$$
$$ = 45.19 	imes {10^{10}}$$ N/C
$$ \simeq 45 	imes {10^{10}}$$

Electrostats & Capacitance

Choose the correct answer: