A charge of total amount Q is distributed over two concentric hollow spheres of radii r and R ( R

Q: A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R ( R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

c Let $q_{1}$ and $q_{2}$ be charge on two spheres of radius $'r'$ and $'R'$ respectively As, $q_{1}+q_{2}=Q$ and $\sigma_{1}=\sigma_{2} \quad$ [Surface charge density are cqual $]$ $\therefore \frac{q_{1}}{r \pi r^{2}}=\frac{q_{2}}{4 \pi R^{2}}$ So, $q_{1}=\frac{Q r^{2}}{R^{2}+r^{2}}$ and $q_{2}=\frac{Q R^{2}}{R^{2}+r^{2}}$ Now, potential, $V=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q_{1}}{r}+\frac{q_{2}}{R}\right]$ $=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{Q r}{R^{2}+r^{2}}+\frac{Q R}{R^{2}+r^{2}}\right]$ $=\frac{Q(R+r)}{R^{2}+r^{2}} \frac{1}{4 \pi \varepsilon_{0}}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R ( R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

A$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{\left( {R - r} \right)Q}}{{\left( {{R^2} + {r^2}} \right)}}$
B$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{\left( {R + r} \right)Q}}{{2\left( {{R^3} + {r^3}} \right)}}$
C$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{\left( {R + r} \right)Q}}{{\left( {{R^2} + {r^2}} \right)}}$
D$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{\left( {R - r} \right)Q}}{{2\left( {{R^2} + {r^2}} \right)}}$

AIEEE 2012,IIT 1981,JEE MAIN 2020, Diffcult

STD 11 Science
NEET
STD 12 - 2. Electric potential and capacitance
Physics

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