Electrostatics Ques 1
- Consider a thin spherical shell of radius $R$ with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\mathbf{E}(r)|$ and the electric potential $V(r)$ with the distance $r$ from the centre, is best represented by which graph?
(2012)
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Answer:
Correct Answer: 1.( d )
Solution:
- For inside points $(r \leq R)$
$ E=0 \Rightarrow V=\text { constant }=\frac{1}{4 \pi \varepsilon_0} \frac{q}{R} $
For outside points ( $r \geq R$ )
$ E=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{r^2} \quad \text { or } \quad E \propto \frac{1}{r^2} $
and
$ V=\frac{1}{4 \pi \varepsilon_0} \frac{q}{r} \quad \text { or } \quad V \propto \frac{1}{r} $
On the surface ( $r=R$ )
$ \begin{aligned} V & =\frac{1}{4 \pi \varepsilon_0} \frac{q}{R} \\ \Rightarrow \quad E & =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{R^2}=\frac{\sigma}{\varepsilon_0} \end{aligned} $
where, $\sigma=\frac{q}{4 \pi R^2}=$ surface charge density corresponding to above equations the correct graphs are shown in option (d).
BETA
