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A solid metal sphere of radius $R$ having charge $q$ is enclosed inside the concentric spherical shell of inner radius $a$ and outer radius $b$ as shown in figure. The approximate variation electric field $\overrightarrow{{E}}$ as a function of distance $r$ from centre $O$ is given by
Solution
Option $(2)$
Considering outer spherical shell is nonconducting
Electric field inside a metal sphere is zero.
${r}<{R} \Rightarrow {E}=0$
${r}>{R} \Rightarrow {E}=\frac{{kQ}}{{r}^{2}}$
Option $(1)$
Considering outer spherical shell is conducting
${r}<{R},{E}=0$
${R} \leq {r}<{a} \quad\quad {E}=\frac{{kQ}}{{r}^{2}}$
${a} \leq {r}<{b},\quad\quad {E}=0$
${r} \geq {b} \quad\quad\quad\quad\quad {E}=\frac{{kQ}}{{r}^{2}}$
Similar Questions
The electric field $E$ is measured at a point $P (0,0, d )$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List-$I$ contains different relations between $E$ and $d$. List-$II$ describes different electric charge distributions, along with their locations. Match the functions in List-$I$ with the related charge distributions in List-$II$.
| List-$I$ | List-$II$ |
| $E$ is independent of $d$ | A point charge $Q$ at the origin |
| $E \propto \frac{1}{d}$ | A small dipole with point charges $Q$ at $(0,0, l)$ and $- Q$ at $(0,0,-l)$. Take $2 l \ll d$. |
| $E \propto \frac{1}{d^2}$ | An infinite line charge coincident with the x-axis, with uniform linear charge density $\lambda$ |
| $E \propto \frac{1}{d^3}$ | Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along ( $y=0$, $z =l$ ) has a charge density $+\lambda$ and the one along $( y =0, z =-l)$ has a charge density $-\lambda$. Take $2 l \ll d$ |
| plane with uniform surface charge density |
