(B) Let $\rho$ be the constant volume charge density. The charge $q$ enclosed by a Gaussian cylinder of radius $r$ and length $L$ is given by $q = \rh

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(B) Let $\rho$ be the constant volume charge density. The charge $q$ enclosed by a Gaussian cylinder of radius $r$ and length $L$ is given by $q = \rho V = \rho (\pi r^2 L)$.According to Gauss's Law,$\oint \vec{E} \cdot d\vec{A} = \frac{q}{\varepsilon_0}$.For the cylindrical Gaussian surface,the flux through the curved surface is $E(2 \pi r L)$,and the flux through the flat ends is zero.Therefore,$E(2 \pi r L) = \frac{\rho \pi r^2 L}{\varepsilon_0}$.Solving for $E$,we get $E = \frac{\rho r}{2 \varepsilon_0}$.Since $\rho$,$2$,and $\varepsilon_0$ are constants,$E \propto r$.

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

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Consider a long uniformly charged cylinder having constant volume charge density $\rho$ and radius $R$. $A$ Gaussian surface is in the form of a cylinder of radius $r$ such that the vertical axis of both cylinders coincide. For a point inside the cylinder $(r < R)$,the electric field is directly proportional to

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$r^{-1}$
B
$r$
C
$r^2$
D
$r^{-2}$

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Class 12

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Electric Charges and Fields

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Electric Field and usage of Gauss's Law

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An 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 $\varepsilon_0 = 8.85 \times 10^{-12} \, C^2 \cdot N^{-1} \cdot m^{-2}$):

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$A$ particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then the time period will be given as (Consider $k$ as Coulomb's constant).

DifficultJEE MAIN 2024

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If an insulated non-conducting sphere of radius $R$ has a uniform charge density $\rho$,the electric field at a distance $r$ from the center of the sphere $(r < R)$ will be:

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As shown in the figure,a charged ball $B$ is suspended from a large charged conducting plate by a silk thread $S$ making an angle $\theta$ with the plate. The surface charge density $\sigma$ of the plate is proportional to ........

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The electric field in a certain region is acting radially outward and is given by $E = Ar$. $A$ charge contained in a sphere of radius $a$ centered at the origin of the field will be given by:

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An 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 $\varepsilon_0 = 8.85 \times 10^{-12} \, C^2 \cdot N^{-1} \cdot m^{-2}$):

$A$ particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then the time period will be given as (Consider $k$ as Coulomb's constant).

If an insulated non-conducting sphere of radius $R$ has a uniform charge density $\rho$,the electric field at a distance $r$ from the center of the sphere $(r < R)$ will be:

As shown in the figure,a charged ball $B$ is suspended from a large charged conducting plate by a silk thread $S$ making an angle $\theta$ with the plate. The surface charge density $\sigma$ of the plate is proportional to ........

The electric field in a certain region is acting radially outward and is given by $E = Ar$. $A$ charge contained in a sphere of radius $a$ centered at the origin of the field will be given by:

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