Electric Charges and Fields - Result Question 27
27. A hollow insulated conduction sphere is given a positive charge of $10 \mu C$. What will be the electric field at the centre of the sphere if its radius is 2 metres?
(a) zero
(b) $5 \mu Cm^{-2}$
(c) $20 \mu Cm^{-2}$
(d) $8 \mu Cm^{-2}$
[1998]
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Answer:
Correct Answer: 27. (a)
Solution:
- (a) Charge resides on the outer surface of a conducting hollow sphere of radius $R$. We consider a spherical surface of radius $r<R$.
By Gauss’s theorem,
$\oint \vec{E} \cdot \vec{d} s=\frac{1}{\varepsilon_0} \times$ charge enclosed
or, $E .4 \pi r^{2}=\frac{1}{\varepsilon_0} \times 0 \Rightarrow E=0$
i.e. electric field inside a hollow sphere is zero.
Electric field inside the charged conducting sphere or shell, $E _{\text{in }}=0$
And for uniformly charged non-conducting sphere,
$ E _{\text{in }}=\frac{1}{4 \pi \epsilon_0} \frac{Q_r}{R^{3}} $
