A unit positive point charge is taken slowly | vedclass

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

Question

(D) The work done by an external agent in moving a charge $q$ slowly from point $A$ to point $B$ is given by $W = q(V_B - V_A)$.Since the charge is a

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(D) The work done by an external agent in moving a charge $q$ slowly from point $A$ to point $B$ is given by $W = q(V_B - V_A)$.Since the charge is a unit positive point charge, $q = 1$, so $W = V_B - V_A$.The potential at a distance $r$ from the center of a uniformly charged dielectric sphere of radius $R$ is:For $r \ge R$, $V(r) = \frac{Q}{4\pi\epsilon_0 r}$, where $Q = \rho \cdot \frac{4}{3}\pi R^3$.Thus, $V(r) = \frac{\rho \cdot \frac{4}{3}\pi R^3}{4\pi\epsilon_0 r} = \frac{\rho R^3}{3\epsilon_0 r}$.Given $r_A = 2R$ and $r_B = 3R$, we have:$V_A = \frac{\rho R^3}{3\epsilon_0 (2R)} = \frac{\rho R^2}{6\epsilon_0}$$V_B = \frac{\rho R^3}{3\epsilon_0 (3R)} = \frac{\rho R^2}{9\epsilon_0}$The work done is $W = |V_B - V_A| = |\frac{\rho R^2}{9\epsilon_0} - \frac{\rho R^2}{6\epsilon_0}| = |\frac{2\rho R^2 - 3\rho R^2}{18\epsilon_0}| = \frac{\rho R^2}{18\epsilon_0}$.Comparing this with $\frac{\rho R^2}{n \epsilon_0}$, we get $n = 18$.

Similar Questions

As shown in the figure,charges $+q$ and $-q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is

$A$ uniformly charged ring of radius $3a$ and total charge $q$ is placed in the $xy$-plane centered at the origin. $A$ point charge $q$ is moving towards the ring along the $z$-axis and has speed $v$ at $z = 4a$. The minimum value of $v$ such that it crosses the origin is

The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$,having same linear charge density $\lambda$ is

For a hollow spherical shell,how does the potential $(V)$ change with respect to the distance $(r)$ from the centre?

Vedclass Test Series

Exam Paper Generator

Online Exam Module