A conducting sphere of radius a has charge Q | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The electrostatic energy $U$ of a system of charges is given by $U = \int \frac{1}{2} \epsilon_0 E^2 dV$.For a conducting sphere of radius $a$ wit

Vedclass · Accepted Answer

$\frac{5}{12} \frac{kQ^2}{a}$

Vedclass · Answer

(A) The electrostatic energy $U$ of a system of charges is given by $U = \int \frac{1}{2} \epsilon_0 E^2 dV$.For a conducting sphere of radius $a$ with charge $Q$,the electric field $E$ is:$1$. $E = 0$ for $r $2$. $E = \frac{kQ}{r^2}$ for $a $3$. $E = 0$ for $2a $4$. $E = \frac{kQ}{r^2}$ for $r > 3a$ (since the shell is neutral,the total charge enclosed is $Q$).The energy stored in the region $a The energy stored in the region $r > 3a$ is $U_2 = \int_{3a}^{\infty} \frac{1}{2} \epsilon_0 (\frac{kQ}{r^2})^2 (4 \pi r^2 dr) = \frac{kQ^2}{2} \int_{3a}^{\infty} \frac{1}{r^2} dr = \frac{kQ^2}{2} [-\frac{1}{r}]_{3a}^{\infty} = \frac{kQ^2}{6a}$.Total energy $U = U_1 + U_2 = \frac{kQ^2}{4a} + \frac{kQ^2}{6a} = \frac{3kQ^2 + 2kQ^2}{12a} = \frac{5kQ^2}{12a}$.

$A$ conducting sphere of radius $a$ has charge $Q$ on it. It is enclosed by a neutral conducting concentric spherical shell having inner radius $2a$ and outer radius $3a$. Find the electrostatic energy of the system.

Similar Questions

Two capacitors of capacities $1 \mu F$ and $C \mu F$ are connected in series and the combination is charged to a potential difference of $120 \ V$. If the charge on the combination is $80 \mu C$,the energy stored in the capacitor of capacity $C$ in $\mu J$ is

As shown in the figure,the work done in moving a charge $q$ from $A$ to $B$ and from $B$ to $C$ is $2 \ J$ and $-3 \ J$ respectively. The work done in moving the charge from $C$ to $A$ will be ...... $J$.

$A$ part of a circuit is shown in the figure. If $V_A - V_B = 4 \, V$,then find the charge on the $4 \, \mu F$ capacitor connected to point $A$. (in $, \mu C$)

Find the equivalent capacitance between $A$ and $B$.

In the circuit shown in the figure,the total charge is $750\, \mu C$ and the voltage across capacitor $C_{2}$ is $20\, V$. If $C_{3} = 8\, \mu F$,then the charge on capacitor $C_{2}$ is $....\mu C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module