A charge q is surrounded by a closed surface consisting of an inverted cone of height h and base rad

English

Gujarati

Hindi

1. Electric Charges and Fields

hard

A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$, and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n q}{6 \epsilon_0}$ (in SI units). The value of $n$ is. . . .

A

$2$

B

$0$

C

$1$

D

$3$

(IIT-2022)

Solution

From Gauss law,

$\phi_{\text {hemisplere }}+\phi_{\text {Cone }}=\frac{ q }{\varepsilon_0}$

Total flux produced from $q$ in $\alpha$ angle

$\phi=\frac{ q }{2 \varepsilon_0}[1-\cos \alpha]$

For hemisphere, $\alpha=\frac{\pi}{2}$

$\phi_{\text {hemisphere }}=\frac{ q }{2 \varepsilon_0}$

From equation $(i)$

$=\frac{ q }{2 \varepsilon_0}+\phi_{\text {cone }}=\frac{ q }{\varepsilon_0}$

$\phi_{\text {cone }}=\frac{ q }{2 \varepsilon_0}$

$\frac{4 q }{6 \varepsilon_0}=\frac{ q }{2 \varepsilon_0}$

$n =3$

Alternatively, $\phi \propto$ no of electric field lines passing through surface $q$ is point charge which has uniformly distributed electric field lines thus half of electric field lines will pass through hemisphere $\&$ other half will pass through conical surface.

Standard 12

Physics

Share

Similar Questions

In figure a point charge $+Q_1$ is at the centre of an imaginary spherical surface and another point charge $+Q_2$ is outside it. Point $P$ is on the surface of the sphere. Let ${\Phi _s}$be the net electric flux through the sphere and ${\vec E_p}$ be the electric field at point $P$ on the sphere. Which of the following statements is $TRUE$ ?

medium

A charge is kept at the central point $P$ of a cylindrical region. The two edges subtend a half-angle $\theta$ at $P$, as shown in the figure. When $\theta=30^{\circ}$, then the electric flux through the curved surface of the cylinder is $\Phi$ If $\theta=60^{\circ}$, then the electric flux through the curved surface becomes $\Phi / \sqrt{n}$, where the value of $n$ is. . . . . . .

normal

(IIT-2024)

The wrong statement about electric lines of force is

easy

A point charge of $+\,12 \,\mu C$ is at a distance $6 \,cm$ vertically above the centre of a square of side $12\, cm$ as shown in figure. The magnitude of the electric flux through the square will be ……. $\times 10^{3} \,Nm ^{2} / C$

medium

(JEE MAIN-2021)

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$-axis in the $y-z$ plane at $z=\frac{\sqrt{3}}{2} a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $A B C D$ lying in the $x-y$ plane with its center at the origin is $\frac{\lambda L }{ n \varepsilon_0}\left(\varepsilon_0=\right.$ permittivity of free space $)$, then the value of $n$ is

medium

(IIT-2015)