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Polarization Vector

Electrostatic...

Question

Electrostatic potential energy of a shell of radius $10 c m .$ When $10 C$ charge is distributed over its surface.

4.5 \times 10^{12} J

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5.4 \times 10^{8} J

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4.5 \times 10^{9} J

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5.4 \times 10^{6} J

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Solution

The correct option is A $4.5 \times 10^{12} J$
$U = \frac{k Q \cdot Q}{2 R}$
$= \frac{9 \times 10^{9} \times 10 \times 10}{2 \times 0.1}$
$U = 4.5 \times 10^{12} J$

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	Column- $I$		Column- $I I$
p.	A thin shell of radius a and having a charge – Q uniformly distributed over its surface as shown	1.	$\frac{1}{8 {πε}_{o}} \times \frac{Q^{2}}{a}$ in magnitude
q.	A thin shell of radius $\frac{5 a}{2}$ having a charge $- Q$ uniformly distributed over its surface and a point charge $- Q$ placed at its centre as shown	2.	$\frac{3}{20 {πε}_{o}} \times \frac{Q^{2}}{a}$ in magnitude
r.	A solid sphere of radius $a$ and having a charge $- Q$ uniformly distributed throughout its volume as shown	3.	$\frac{27 Q}{80 π ε_{o}} \times \frac{Q^{2}}{a}$ in magnitute
s.	A solid sphere of radius a and having a charge – Q uniformly distributed throughout its volume. The solid sphere is surrounded by a concentric thin uniformly charged spherical shell of radius $2 a$ and carrying charge $- Q$ as shown	4.	$\frac{27 Q}{60 π ε_{o}} \times \frac{Q^{2}}{a}$ in magnitude

U_{1}

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Column-I	Column-II
(P) A thin shell of radius $a$ and having a charge $- Q$ uniformly distributed over its surface as shown	(1) $\frac{1}{8 π ϵ_{0}} \frac{Q^{2}}{a}$ in magnitude
(Q) A thin shell of radius $\frac{5 a}{2}$ and having a charge $- Q$ uniformly distributed over its surface and a point charge $- Q$ is brought from infinity and placed at its centre as shown.	(2) $\frac{3}{20 π ϵ_{0}} \frac{Q^{2}}{a}$ in magnitude
(R) A solid sphere of radius $a$ and having a charge $- Q$ uniformly distributed throughout its volume as shown.	(3) $\frac{27 Q}{80 π ϵ_{0}} \frac{Q^{2}}{a}$ in magnitude
(S) A solid sphere of radius a and having a charge $- Q$ uniformly distributed throughout its volume. The solid sphere is surrounded by a concentric thin uniformly charged spherical shell of radius 2a and carrying charge $- Q$ as shown	(4) $\frac{5}{27 π ϵ_{0}} \frac{Q^{2}}{a}$ in magnitude

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