(B) According to Gauss's Law,the electric field at a distance $R$ from the center of a spherical charge distribution is given by $E = \frac{k q_{enclo

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$\frac{3Q}{4\pi \varepsilon_0 R^2}$

(B) According to Gauss's Law,the electric field at a distance $R$ from the center of a spherical charge distribution is given by $E = \frac{k q_{enclosed}}{R^2}$.For the region $a The charge enclosed by this Gaussian surface is only the charge on the solid metal sphere,which is $+3Q$.The conducting shell (charge $-Q$) is outside the Gaussian surface,so it contributes zero to the electric field at distance $R$ inside the shell.Therefore,the electric field $E$ is given by:$E = \frac{1}{4\pi \varepsilon_0} \cdot \frac{3Q}{R^2} = \frac{3Q}{4\pi \varepsilon_0 R^2}$.

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

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$A$ solid metal sphere has a charge of $+3Q$. It is concentric with a conducting spherical shell having a charge of $-Q$. The radius of the sphere is $a$ and the radius of the shell is $b$ $(b > a)$. The electric field at a distance $R$ from the center $(a < R < b)$ is .......

A
$\frac{4Q}{2\pi \varepsilon_0 R^2}$
B
$\frac{3Q}{4\pi \varepsilon_0 R^2}$
C
$\frac{3Q}{2\pi \varepsilon_0 R^2}$
D
$\frac{Q}{2\pi \varepsilon_0 R}$

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Electric Charges and Fields

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Electric Field and usage of Gauss's Law

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DifficultAP EAMCET 2021

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The electric potential $V(x)$ in a region around the origin is given by $V(x) = 4x^2 \text{ V}$. The electric charge enclosed in a cube of $1 \text{ m}$ side with its centre at the origin is (in coulomb):

MediumAIEEE 2012

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Let $\rho (r) = \frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $p$ inside the sphere at distance $r_1$ from the centre of the sphere,the magnitude of the electric field is:

DifficultAIEEE 2009

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$A$ hollow cylinder has a charge $q$ within it. If $\phi$ is the electric flux in units of $V-m$ associated with the curved surface $B,$ the flux linked with the plane surface $A$ in units of $V-m$ will be

MediumAIPMT 2007

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The electric field at a distance $R$ from the surface of a uniformly charged nonconducting sphere of radius $R$ is $20 \,V/m$. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is $.... \,V/m$.

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$A$ solid metal sphere has a charge of $+3Q$. It is concentric with a conducting spherical shell having a charge of $-Q$. The radius of the sphere is $a$ and the radius of the shell is $b$ $(b > a)$. The electric field at a distance $R$ from the center $(a < R < b)$ is .......

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An $100 \ eV$ electron is fired directly towards a large metal plate having surface charge density $-2 \times 10^{-6} \ C \ m^{-2}$. The distance from where the electron is projected,so that it just fails to strike the plate,is: (in $mm$)

The electric potential $V(x)$ in a region around the origin is given by $V(x) = 4x^2 \text{ V}$. The electric charge enclosed in a cube of $1 \text{ m}$ side with its centre at the origin is (in coulomb):

Let $\rho (r) = \frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $p$ inside the sphere at distance $r_1$ from the centre of the sphere,the magnitude of the electric field is:

$A$ hollow cylinder has a charge $q$ within it. If $\phi$ is the electric flux in units of $V-m$ associated with the curved surface $B,$ the flux linked with the plane surface $A$ in units of $V-m$ will be

The electric field at a distance $R$ from the surface of a uniformly charged nonconducting sphere of radius $R$ is $20 \,V/m$. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is $.... \,V/m$.

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