A solid ball of radius $R$ has a charge density $\rho $ given by $\rho = {\rho _0}\left( {1 - \frac{r}{R}} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is
A solid ball of radius $R$ has a charge density $\rho $ given by $\rho = {\rho _0}\left( {1 - \frac{r}{R}} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is
- [JEE MAIN 2018]
- A
$\frac{{{\rho _0}{R^3}}}{{{\varepsilon _0}{r^2}}}$
- B
$\frac{{{4\rho _0}{R^3}}}{{{3\varepsilon _0}{r^2}}}$
- C
$\frac{{{3\rho _0}{R^3}}}{{{4\varepsilon _0}{r^2}}}$
- D
$\frac{{{\rho _0}{R^3}}}{{{12\varepsilon _0}{r^2}}}$
Similar Questions
Two parallel infinite line charges with linear charge densities $+\lambda\; \mathrm{C} / \mathrm{m}$ and $-\lambda\; \mathrm{C} / \mathrm{m}$ are placed at a distance of $2 \mathrm{R}$ in free space. What is the electric field mid-way between the two line charges?
Two parallel infinite line charges with linear charge densities $+\lambda\; \mathrm{C} / \mathrm{m}$ and $-\lambda\; \mathrm{C} / \mathrm{m}$ are placed at a distance of $2 \mathrm{R}$ in free space. What is the electric field mid-way between the two line charges?
- [NEET 2019]
Which of the following graphs shows the variation of electric field $E$ due to a hollow spherical conductor of radius $R$ as a function of distance $r$ from the centre of the sphere
Which of the following graphs shows the variation of electric field $E$ due to a hollow spherical conductor of radius $R$ as a function of distance $r$ from the centre of the sphere
Let a total charge $2Q$ be distributed in a sphere of radius $R$, with the charge density given by $\rho(r) = kr$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance, $a$, from the centre. If $A$ and $B$ do not experience any force, then
Let a total charge $2Q$ be distributed in a sphere of radius $R$, with the charge density given by $\rho(r) = kr$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance, $a$, from the centre. If $A$ and $B$ do not experience any force, then
- [JEE MAIN 2019]
Two fixed, identical conducting plates $(\alpha $ and $\beta )$, each of surface area $S$ are charged to $-\mathrm{Q}$ and $\mathrm{q}$, respectively, where $Q{\rm{ }}\, > \,{\rm{ }}q{\rm{ }}\, > \,{\rm{ }}0.$ A third identical plate $(\gamma )$, free to move is located on the other side of the plate with charge $q$ at a distance $d$ as per figure. The third plate is released and collides with the plate $\beta $. Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst $\beta $ and $\gamma $.
$(a)$ Find the electric field acting on the plate $\gamma $ before collision.
$(b)$ Find the charges on $\beta $ and $\gamma $ after the collision.
$(c)$ Find the velocity of the plate $\gamma $ after the collision and at a distance $d$ from the plate $\beta $.
Two fixed, identical conducting plates $(\alpha $ and $\beta )$, each of surface area $S$ are charged to $-\mathrm{Q}$ and $\mathrm{q}$, respectively, where $Q{\rm{ }}\, > \,{\rm{ }}q{\rm{ }}\, > \,{\rm{ }}0.$ A third identical plate $(\gamma )$, free to move is located on the other side of the plate with charge $q$ at a distance $d$ as per figure. The third plate is released and collides with the plate $\beta $. Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst $\beta $ and $\gamma $.
$(a)$ Find the electric field acting on the plate $\gamma $ before collision.
$(b)$ Find the charges on $\beta $ and $\gamma $ after the collision.
$(c)$ Find the velocity of the plate $\gamma $ after the collision and at a distance $d$ from the plate $\beta $.
Obtain Coulomb’s law from Gauss’s law.
Obtain Coulomb’s law from Gauss’s law.