Electric Charges And Fields Ques 42
42. Two metallic spheres of radii $1$ $ cm$ and $3$ $ cm$ are given charges of $-1 \times 10^{-2} C$ and $5 \times 10^{-2} C$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is :
[2012 M]
(a) $2 \times 10^{-2} C$
(b) $3 \times 10^{-2} C$
(c) $4 \times 10^{-2} C$
(d) $1 \times 10^{-2} C$
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Answer:
Correct Answer: 42.(b)
Solution:
- (b) At equilibrium potential of both spheres becomes same if charge of sphere one $x$ and other sphere $(Q-x)$ then
where $Q=4 \times 10^{-2} C$
$V_1=V_2$
$\frac{k x}{1\ \text{cm}}=\frac{k(Q-x)}{3\ \text{cm}}$
$3 x=Q-x \Rightarrow 4 x=Q$
$x=\frac{Q}{4}=\frac{4 \times 10^{-2}}{4} C=1 \times 10^{-2}$
$Q^{\prime}=Q-x=3 \times 10^{-2} C$
Charge given to a conductor always resides on its outer surface. If surface is uniform the charge distributes uniformly on the surface and for irregular surface the distribution of charge i.e., charge density is not uniform. It is maximum where the radius of curvature is minimum and vice-versa i.e., $\sigma \propto \frac{1}{R}$.
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