$A$ non-conducting solid sphere of radius $R$ has a uniform volume charge density $\rho$. The electric potential at the center of the sphere is related to the potential at the surface and outside the sphere due to this uniform charge distribution.
Statement-$1$: When a charge $q$ is moved from the surface to the center of the sphere,the change in its potential energy is $q\rho R^2 / 6\varepsilon_0$.
Statement-$2$: The electric field at a distance $r$ $(r < R)$ from the center of the sphere is $\rho r / 3\varepsilon_0$.
Statement-$1$: When a charge $q$ is moved from the surface to the center of the sphere,the change in its potential energy is $q\rho R^2 / 6\varepsilon_0$.
Statement-$2$: The electric field at a distance $r$ $(r < R)$ from the center of the sphere is $\rho r / 3\varepsilon_0$.
- AStatement-$1$ is true,Statement-$2$ is true,and Statement-$2$ is the correct explanation for Statement-$1$.
- BStatement-$1$ is true,Statement-$2$ is true,and Statement-$2$ is not the correct explanation for Statement-$1$.
- CStatement-$1$ is true,Statement-$2$ is false.
- DStatement-$1$ is false,Statement-$2$ is true.
Explore More
Similar Questions
Match List-$I$ with List-$II$:
List-$I$ List-$II$ $(A)$ Electric field inside (distance $r < R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$. $(I)$ $\sigma / \varepsilon_0$ $(B)$ Electric field at distance $r$ from a uniformly charged infinite plane sheet with surface charge density $\sigma$. $(II)$ $\sigma / 2 \varepsilon_0$ $(C)$ Electric field outside (distance $r > R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$. $(III)$ $0$ $(D)$ Electric field between $2$ oppositely charged infinite plane parallel sheets with uniform surface charge density $\sigma$. $(IV)$ $\frac{\sigma R^2}{\varepsilon_0 r^2}$
Choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| $(A)$ Electric field inside (distance $r < R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$. | $(I)$ $\sigma / \varepsilon_0$ |
| $(B)$ Electric field at distance $r$ from a uniformly charged infinite plane sheet with surface charge density $\sigma$. | $(II)$ $\sigma / 2 \varepsilon_0$ |
| $(C)$ Electric field outside (distance $r > R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$. | $(III)$ $0$ |
| $(D)$ Electric field between $2$ oppositely charged infinite plane parallel sheets with uniform surface charge density $\sigma$. | $(IV)$ $\frac{\sigma R^2}{\varepsilon_0 r^2}$ |
Choose the correct answer from the options given below:
$A$ spherical shell with an inner radius $a$ and an outer radius $b$ is made of conducting material. $A$ point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Find the final charge distribution on the surfaces.
Medium
View SolutionAn infinitely long thin straight wire has a uniform linear charge density of $\frac{1}{3} \, C \cdot m^{-1}$. The magnitude of the electric field intensity at a point $18 \, cm$ away is (given $\varepsilon_0 = 8.85 \times 10^{-12} \, C^2 \cdot N^{-1} \cdot m^{-2}$):
DifficultAP EAMCET 2009
View Solution$A$ spherically symmetric charge distribution is considered with charge density varying as
$\rho(r)=\begin{cases} \rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text{for } r \leq R \\ 0 & \text{for } r>R \end{cases}$
Where,$r (r < R)$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be.
$\rho(r)=\begin{cases} \rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text{for } r \leq R \\ 0 & \text{for } r>R \end{cases}$
Where,$r (r < R)$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be.
DifficultJEE MAIN 2022
View SolutionConsider a sphere of radius $R$ with charge density distributed as:
$\rho(r) = kr$ for $r \leq R$
$\rho(r) = 0$ for $r > R$
$(a)$ Find the electric field at all points $r$.
$(b)$ Suppose the total charge on the sphere is $2e$ where $e$ is the elementary charge. Where can two protons be embedded such that the force on each of them is zero? Assume that the introduction of the protons does not alter the charge distribution.
$\rho(r) = kr$ for $r \leq R$
$\rho(r) = 0$ for $r > R$
$(a)$ Find the electric field at all points $r$.
$(b)$ Suppose the total charge on the sphere is $2e$ where $e$ is the elementary charge. Where can two protons be embedded such that the force on each of them is zero? Assume that the introduction of the protons does not alter the charge distribution.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo