(A) According to Gauss's Law,for a uniformly charged spherical shell of radius $R$ and total charge $Q$:$1$. For points outside the shell $(r > R)$,th

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$F = \frac{1}{4 \pi \varepsilon_{0}} \frac{Qq}{r^{2}}$ for $r > R$

(A) According to Gauss's Law,for a uniformly charged spherical shell of radius $R$ and total charge $Q$:$1$. For points outside the shell $(r > R)$,the shell behaves as if all its charge is concentrated at the centre. Thus,the electric field is $E = \frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r^{2}}$. The force on a charge $q$ is $F = qE = \frac{1}{4 \pi \varepsilon_{0}} \frac{Qq}{r^{2}}$.$2$. For points inside the shell $(r Comparing these results with the given options,statement $A$ is correct.

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

Difficult

Consider the force $F$ on a charge $q$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$,if $q$ is placed at distance $r$ from the centre of the shell?

JEE MAIN 2020 All JEE MAIN

A
$F = \frac{1}{4 \pi \varepsilon_{0}} \frac{Qq}{r^{2}}$ for $r > R$
B
$\frac{1}{4 \pi \varepsilon_{0}} \frac{qQ}{R^{2}} > F > 0$ for $r < R$
C
$F = \frac{1}{4 \pi \varepsilon_{0}} \frac{Qq}{r^{2}}$ for all $r$
D
$F = \frac{1}{4 \pi \varepsilon_{0}} \frac{Qq}{R^{2}}$ for $r < R$

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Electric Charges and Fields

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Electric Field and usage of Gauss's Law

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Consider the force $F$ on a charge $q$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$,if $q$ is placed at distance $r$ from the centre of the shell?

Similar Questions

$A$ long cylindrical volume contains a uniformly distributed charge of density $\rho \; C m^{-3}$. The electric field inside the cylindrical volume at a distance $x = \frac{2 \varepsilon_{0}}{\rho} \; m$ from its axis is $....... V m^{-1}$.

The electric field at a distance of $20 \ cm$ from the center of a uniformly charged dielectric sphere of radius $R = 10 \ cm$ is $100 \ V/m$. What will be the electric field $E$ at a distance of $3 \ cm$ from the center of the sphere (in $V/m$)?

$A$ 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.

Let $P(r) = \frac{Q}{\pi R^4} r$ 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

If the linear charge density of a cylinder is $4 \mu C m^{-1}$,then the electric field intensity at a point $3.6 \ cm$ from the axis is:

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