A total charge Q is distributed between two c | 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 inner and outer shells respectively. Given $Q = q_1 + q_2$ ... $(i)$Since surface charge densities are e

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 inner and outer shells respectively. Given $Q = q_1 + q_2$ ... $(i)$Since surface charge densities are equal,$\sigma_1 = \sigma_2$,so $\frac{q_1}{4\pi r^2} = \frac{q_2}{4\pi R^2} \implies \frac{q_1}{q_2} = \frac{r^2}{R^2}$ ... $(ii)$From $(i)$ and $(ii)$,we get $q_1 = \frac{Q r^2}{R^2 + r^2}$ and $q_2 = \frac{Q R^2}{R^2 + r^2}$.The potential at the center is the sum of potentials due to both shells: $V = \frac{1}{4\pi \varepsilon_0} \left[ \frac{q_1}{r} + \frac{q_2}{R} \right]$.Substituting the values of $q_1$ and $q_2$: $V = \frac{1}{4\pi \varepsilon_0} \left[ \frac{Q r^2}{r(R^2 + r^2)} + \frac{Q R^2}{R(R^2 + r^2)} \right] = \frac{1}{4\pi \varepsilon_0} \left[ \frac{Qr}{R^2 + r^2} + \frac{QR}{R^2 + r^2} \right]$.Thus,$V = \frac{Q(R + r)}{4\pi \varepsilon_0(R^2 + r^2)}$.

$A$ 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?

Similar Questions

Two point charges $-20 \,\mu C$ and $+40 \,\mu C$ are separated by a distance $r$. At which region$(s)$ will the electric potential be zero?

Which physical quantities are represented by $X$ and $Y$ in the given graph? ($Y$ represents the first quantity.)

Calculate the work done in taking a charge $q_0 = -2 \times 10^{-9} \, C$ from point $A$ to point $B$ via point $C$,as shown in the diagram. The source charge $q = 8 \, mC$ is located at the origin $O$. (in $, J$)

The electric potential $V$ of a charged spherical shell depends on the distance $r$ from its center. Which of the following graphs represents this dependence?

$A$ sphere with charge $Q$ is placed concentrically inside an uncharged spherical shell. The potential difference between them is $V$. Now,if a charge of $-3Q$ is given to the spherical shell,what will be the potential difference between them?

Vedclass Test Series

Exam Paper Generator

Online Exam Module