A total electric charge Q is distributed on t | vedclass

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

Question

(C) The electrical potential energy $U$ of a charged sphere can be calculated by considering the work done in bringing small charge elements $dq$ from

Vedclass · Accepted Answer

$\frac{1}{2} \frac{k Q^2}{R}$

Vedclass · Answer

(C) The electrical potential energy $U$ of a charged sphere can be calculated by considering the work done in bringing small charge elements $dq$ from infinity to the surface of the sphere.Alternatively,we can use the average potential method.Initially,when there is no charge on the sphere,the potential $V_1 = 0$.When the total charge $Q$ is on the sphere,the potential $V_2 = \frac{k Q}{R}$.The average potential $V$ during the charging process is $V = \frac{V_1 + V_2}{2} = \frac{0 + \frac{k Q}{R}}{2} = \frac{k Q}{2 R}$.The total potential energy $U$ is the work done to charge the sphere,which is given by $U = \int_0^Q V(q) dq = \int_0^Q \frac{k q}{R} dq = \frac{k}{R} \left[ \frac{q^2}{2} \right]_0^Q = \frac{1}{2} \frac{k Q^2}{R}$.

$A$ total electric charge $Q$ is distributed on the surface of a sphere of radius $R$. What is the electrical potential energy of this system?

Similar Questions

Three concentric charged metallic spherical shells $A$,$B$,and $C$ have radii $a$,$b$,and $c$ (where $a < b < c$) and surface charge densities $+\sigma$,$-\sigma$,and $+\sigma$ respectively. The potential $V_A$ at the surface of shell $A$ is ($\epsilon_0$ = permittivity of free space).

$A$ proton is accelerated through $50,000 \, V$. Its energy will increase by

$A$ charge of $5\,C$ is given a displacement of $0.5\,m$. The work done in the process is $10\,J$. The potential difference between the two points will be.......$V$

Two point charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively. The electric potential at a point $(0,0, z)$,where $z>a$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module