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 $a$
Show Answer
Answer:
Correct Answer: 12. (c)
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).
