Question 111: Electrostats & Capacitance

Question

Which of the following diagram represents the variation of the electric field with distance r from the centre of a uniformly charged non-conducting sphere of radius R?

Accepted Answer

The electric field intensity at a point lying outside the sphere (non-conducting) is
$$E = {1 \over {4\pi {\varepsilon _0}}}\,.\,{q \over {{r^2}}}$$
$$ \Rightarrow E \propto {1 \over {{r^2}}}$$
The electric field intensity at the sphere $$(r=R)$$,
$$\begin{aligned}
& E=\frac{1}{4 \pi \varepsilon_0} \frac{q}{R^2} \
\Rightarrow & E \propto \frac{1}{R^2}
\end{aligned}$$
where, $$R$$ being the radius of sphere.
The electric field intensity inside the sphere is
$$\begin{array}{ll}
\Rightarrow & E=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q r}{R^3} \
\Rightarrow & E \propto r
\end{array}$$
At the centre of sphere, $$E=0$$
Hence, option (c) is correct representation.

Answer

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Answer

Electrostats & Capacitance

Which of the following diagram represents the variation of the electric field with distance r from the centre of a uniformly charged non-conducting sphere of radius R?

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