If on the concentric hollow spheres of radii | vedclass

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

Question

(D) Let $q_1$ and $q_2$ be the charges on the spheres of radii $r$ and $R$ respectively. Given that $q_1 + q_2 = Q$.Since surface charge densities are

Vedclass · Accepted Answer

$\frac{Q(R + r)}{4\pi \varepsilon_0(R^2 + r^2)}$

Vedclass · Answer

(D) Let $q_1$ and $q_2$ be the charges on the spheres of radii $r$ and $R$ respectively. Given that $q_1 + q_2 = Q$.Since surface charge densities are equal,$\sigma = \frac{q_1}{4\pi r^2} = \frac{q_2}{4\pi R^2}$.This implies $\frac{q_1}{r^2} = \frac{q_2}{R^2}$,so $q_1 = q_2 \frac{r^2}{R^2}$.Substituting this into the total charge equation: $q_2 \frac{r^2}{R^2} + q_2 = Q \implies q_2 \left( \frac{r^2 + R^2}{R^2} \right) = Q \implies q_2 = \frac{Q R^2}{R^2 + r^2}$.Similarly,$q_1 = \frac{Q r^2}{R^2 + r^2}$.The potential at the common centre is the sum of potentials due to both spheres: $V = \frac{1}{4\pi \varepsilon_0} \left( \frac{q_1}{r} + \frac{q_2}{R} \right)$.Substituting the values of $q_1$ and $q_2$: $V = \frac{1}{4\pi \varepsilon_0} \left( \frac{Q r^2}{r(R^2 + r^2)} + \frac{Q R^2}{R(R^2 + r^2)} \right)$.$V = \frac{1}{4\pi \varepsilon_0} \left( \frac{Q r}{R^2 + r^2} + \frac{Q R}{R^2 + r^2} \right) = \frac{Q(R + r)}{4\pi \varepsilon_0(R^2 + r^2)}$.

If on the concentric hollow spheres of radii $r$ and $R$ $(R > r)$ the charge $Q$ is distributed such that their surface charge densities are the same,then the potential at their common centre is:

Similar Questions

$A$ total charge $Q$ is distributed between two concentric spherical shells of radii $r$ and $R$ $(R > r)$ such that their surface charge densities are equal. What is the electric potential at their common center?

Three charges $q, \sqrt{2}q$,and $2q$ are placed at the corners $A, B$,and $C$ respectively of a square $ABCD$ of side length $a$. Find the electric potential at point $D$.

Point charges $q_1 = 2\,\mu C$ and $q_2 = -1\,\mu C$ are kept at points $x = 0$ and $x = 6$ respectively. Electrical potential will be zero at points

The electric potential at a distance of $R/2$ from the center of a charged conducting sphere of radius $R$ is .......

$A$ charge $Q$ is distributed over three concentric spherical shells of radii $a, b, c$ $(a < b < c)$ such that their surface charge densities are equal to one another. The total potential at a point at distance $r$ from their common centre,where $r < a$,would be

Vedclass Test Series

Exam Paper Generator

Online Exam Module