An electric charge q is placed at centre of a cube of side α . electric flux on one of its faces wi

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1. Electric Charges and Fields

easy

An electric charge $q$ is placed at the centre of a cube of side $\alpha $. The electric flux on one of its faces will be

$\frac{q}{{6{\varepsilon _0}}}$

$\frac{q}{{{\varepsilon _0}{a^2}}}$

$\frac{q}{{4\pi {\varepsilon _0}{a^2}}}$

$\frac{q}{{{\varepsilon _0}}}$

(AIIMS-2001)

Solution

(a) By Gauss's theorem.

Net flux through the cube ${\varphi _{net}} = \frac{Q}{{{\varepsilon _0}}};$ so flux through one face ${\varphi _{face}} = \frac{q}{{6{\varepsilon _0}}}$

Standard 12

Physics

Let the electrostatic field $E$ at distance $r$ from a point charge $q$ not be an inverse square but instead an inverse cubic, e.g. $E =k \cdot \frac{q}{r^{3}} \hat{ r }$, here $k$ is a constant.

Consider the following two statements:

$(I)$ Flux through a spherical surface enclosing the charge is $\phi=q_{\text {enclosed }} / \varepsilon_{0}$.

$(II)$ A charge placed inside uniformly charged shell will experience a force.

Which of the above statements are valid?

normal

(KVPY-2017)

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. . . .

hard

(IIT-2022)

Electric flux through a surface of area $100$ $m^2$ lying in the $xy$ plane is (in $V-m$) if $\vec E = \hat i + \sqrt 2 \hat j + \sqrt 3 \hat k$

medium

Gauss’s law states that

medium

(AIIMS-2017)

Is electric flux scalar or vector ?