Electrostatics 1 Question 12
12. The electric field at $r=R$ is
(2008, 4M)
(a) independent of $a$
(b) directly proportional to $a$
(c) directly proportional to $a^{2}$
(d) inversely proportional to $a$
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Answer:
Correct Answer: 12. (a)
Solution:
- At $r=R$, from Gauss’s law
$$ E\left(4 \pi R^{2}\right)=\frac{q_{\text {net }}}{\varepsilon_{0}}=\frac{Z e}{\varepsilon_{0}} \text { or } E=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Z e}{R^{2}} $$
$E$ is independent of $a$.
$\therefore$ Correct option is (a).
