A hollow spherical conductor of radius 12 cm is charged to $6*10^{-6}C$. Find the electric field strength at the surface of sphere, inside the sphere at $8\;cm$ and at distance $15 \;cm$ from the sphere.

Given,

Radius of the charged sphere $(R) = 12 \; cm$

Charge $(q) = 6 * 10^{-6}\; C$

Electric field intensity $(E) = ?$

i) On the surface

$E = $$\frac{1}{4 \pi \epsilon_0} \frac{q}{R^2}$$ \;=\; 9 \;*\; 10^9 \;*\; $$\frac{6 \;*\; 10^{-6}}{(0.12)^2}$$ = 3.75 * 10^{6}\;N/C$

ii) Inside the sphere,

$E = 0$;          Because charge enclosed by Gaussian surface is zero.

iii) Outside the sphere at distance $15 \;cm$

i.e. $r = 12 + 15 = 27\;cm = 0.27\;m$

$E = $$\frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}$$ = 9 * 10^9 \;*\; $$\frac{6 \;*\; 10^6}{(0.27)^2}$$ = 7.41 \;*\; 10^5\; N/C$

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