A solid sphere of radius $1\;cm$ is carrying a charge of $2\;C$. Find the electric field intensity at the center, on its surface and at a point $2\;cm$ from the center of the charged sphere.

Given,

Radius of the charged sphere $(R) = 1 \; cm = 0.01\;m$

Charge $(q) = 2\; C$

Electric field intensity $(E) = ?$

i) At the center of the sphere,

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

ii) At the surface of the sphere,

$E = $$\frac{1}{4 \pi \epsilon_0} \frac{q}{R^2}$$ \;=\; 9 \;*\; 10^9 \;*\; $$\frac{2}{(0.01)}$$ = 1.8 * 10^{12}\;N/C$

iii) At $2\;cm$ from the center,

i.e. $r = 2 = 2\;cm = 0.02\;m$

$E = $$\frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}$$ = 9 * 10^9 \;*\; $$\frac{2}{(0.02)}$$ = 9 \;*\; 10^{11}\; N/C$

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