Identical charges (-q) are placed at each cor | vedclass

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

Question

(D) The length of the body diagonal of a cube with side $b$ is $\sqrt{3}b$.Therefore,the distance from the center of the cube to each corner is $r = \

Vedclass · Accepted Answer

$\frac{-4q^2}{\sqrt{3}\pi\varepsilon_0 b}$

Vedclass · Answer

(D) The length of the body diagonal of a cube with side $b$ is $\sqrt{3}b$.Therefore,the distance from the center of the cube to each corner is $r = \frac{\sqrt{3}b}{2}$.The electrostatic potential energy $U$ of a charge $q_2$ at a distance $r$ from a charge $q_1$ is given by $U = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r}$.Since there are $8$ such charges of $(-q)$ at the corners and a charge $(+q)$ at the center,the total potential energy is:$U = 8 	imes \left[ \frac{1}{4\pi\varepsilon_0} \cdot \frac{(-q)(q)}{\frac{\sqrt{3}b}{2}} ight]$$U = 8 	imes \left[ \frac{1}{4\pi\varepsilon_0} \cdot \frac{-2q^2}{\sqrt{3}b} ight]$$U = \frac{-16q^2}{4\sqrt{3}\pi\varepsilon_0 b} = \frac{-4q^2}{\sqrt{3}\pi\varepsilon_0 b}$.

Identical charges $(-q)$ are placed at each corner of a cube of side $b$. The electrostatic potential energy of a charge $(+q)$ placed at the center of the cube is:

Similar Questions

Two points $P$ and $Q$ are maintained at the potentials of $10 \ V$ and $-4 \ V$,respectively. The work done in moving $100$ electrons from $P$ to $Q$ is

$A$ point charge $q$ of mass $m$ is placed at the center of a ring of radius $R$ carrying a charge $Q$. When it is slightly displaced,the point charge accelerates to infinity along the $x$-axis. The ultimate speed of the point charge is .......

Equal charges are given to two spheres of different radii. The potential will

Explain electrostatic potential energy difference and give the noteworthy comments on it.

Two points $P$ and $Q$ are at potentials of $10 \ V$ and $-4 \ V$ respectively. The work done in moving $100$ electrons from $P$ to $Q$ is .....

Vedclass Test Series

Exam Paper Generator

Online Exam Module