(B) For a solid sphere of radius $R$ with uniform volume charge density $\rho$,the electric field $E$ is given by:$1$. Inside the sphere $(r < R)$: $E

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The object must be a solid sphere with uniform volume charge density.

(B) For a solid sphere of radius $R$ with uniform volume charge density $\rho$,the electric field $E$ is given by:$1$. Inside the sphere $(r $2$. Outside the sphere $(r \geq R)$: $E = \frac{Q}{4\pi\epsilon_0 r^2}$,which implies $E \propto \frac{1}{r^2}$.The given graph shows $E$ increasing linearly with $r$ until a maximum value at the surface,and then decreasing as $1/r^2$ for $r > R$. This behavior is characteristic of a uniformly charged solid sphere.

Class 12 Physics Electric Charges and Fields Electric Field and usage of Gauss's Law

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The figure shows the graph of electric field $E(r)$ versus distance $(r)$ from the center of an object. Therefore,...

A
The object must be a charged conducting solid.
B
The object must be a solid sphere with uniform volume charge density.
C
The object must be a solid cube with uniform volume charge density.
D
The object must be a charged conducting sphere.

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Electric Charges and Fields

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Electric Field and usage of Gauss's Law

$A$ sphere of radius $R$ has a volume charge density $\rho = k r$, where $r$ is the distance from the center of the sphere and $k$ is a constant. The magnitude of the electric field at the surface of the sphere is given by ($\varepsilon_{0} =$ permittivity of free space):

DifficultWBJEE 2013

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$A$ hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$?

EasyAIPMT 1998

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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:

MediumJEE MAIN 2025

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The electrostatic potential inside a charged spherical ball is given by $\Phi = a r^2 + b$,where $r$ is the distance from the centre and $a, b$ are constants. Then,the charge density inside the ball is ($\varepsilon_0 =$ permittivity in free space).

DifficultTS EAMCET 2020

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$A$ solid metallic sphere has a charge $+3 Q$. Concentric with this sphere is a conducting spherical shell having charge $-Q$. The radius of the sphere is $A$ and that of the spherical shell is $B$ $(B > A)$. The electric field at a distance $R$ $(A < R < B)$ from the centre is $(\varepsilon_0 = \text{permittivity of vacuum})$

MediumMHT CET 2023

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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 $\sigma$.	$(IV)$ $\frac{\sigma R^2}{\varepsilon_0 r^2}$

The figure shows the graph of electric field $E(r)$ versus distance $(r)$ from the center of an object. Therefore,...

Similar Questions

$A$ sphere of radius $R$ has a volume charge density $\rho = k r$, where $r$ is the distance from the center of the sphere and $k$ is a constant. The magnitude of the electric field at the surface of the sphere is given by ($\varepsilon_{0} =$ permittivity of free space):

$A$ hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$?

The electrostatic potential inside a charged spherical ball is given by $\Phi = a r^2 + b$,where $r$ is the distance from the centre and $a, b$ are constants. Then,the charge density inside the ball is ($\varepsilon_0 =$ permittivity in free space).

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