Electrostatics 1 Question 16
17. A non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its centre
(1998, 2M)
(a) increases as $r$ increases for $r<R$
(b) decreases as $r$ increases for $0<r<\infty$
(c) decreases as $r$ increases for $R<r<\infty$
(d) is discontinuous at $r=R$
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Answer:
Correct Answer: 17. (a,c)
Solution:
- Inside the sphere $E=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{R^{3}} r$
$$ \Rightarrow \quad E \propto r \text { for } r \leq R $$
i.e. $E$ at centre $=0$ as $r=0$ and $E$ at surface $=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{R^{2}}$
$$ \text { as } \quad r=R $$
Outside the sphere
or
$$ \begin{aligned} & E=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{r^{2}} \text { for } r \geq R \\ & E \propto \frac{1}{r^{2}} \end{aligned} $$
Thus, variation of electric field $(E)$ with distance $(r)$ from the centre will be as shown
