Question

A charge $Q$ is kept at the corner of a cube. If the net flux through the cube is $\varphi$, the electric flux passing through one of those faces not touching the charge will be

• A. $\frac{\varphi }{3}$
• B. $\frac{\varphi }{6}$
• C. $\frac{\varphi }{4}$
• D. $\frac{\varphi }{8}$

Answer 1

The correct option is A $\frac{\varphi }{3}$


The electric field lines emerging from charge $Q$ radially outward will be tangential to the three faces in contact with the charge. Thus face $ABHF,ABCD$ and $ADEF$ will not have any field lines crossing through them.
So flux through these faces will be zero
that is,
${\varphi }_{ABHF}={\varphi }_{ABCD}={\varphi }_{ADEF}=0$
Let the flux through remaining faces is ${\varphi }^{\prime }$ .
So we can say that,
${\varphi }^{\prime }+3{\varphi }_{ABCD}=\varphi$
$\Rightarrow {\varphi }^{\prime }+0=\varphi$

Since the remaining faces are not touching the charge is located symmetrically with respect to corner charge.

Thus flux through each of the remaining untouched face will be equal, let it be ${\varphi }_1$

According to question
$3{\varphi }_1={\varphi }^{\prime }$
$\Rightarrow {\varphi }_1=\frac{{\varphi }^{\prime }}{3}$
$\Rightarrow {\varphi }_1=\frac{\varphi }{3}$
Hence, answer (a) is correct.

$\begin{array}{c}\text{Why this question}?\\ \text{Tip: Whenever a charge is placed on}\\ \text{a geometrical shape, identify the}\\ \text{surface through which electric field}\\ \text{passes tangentially such that}\varphi =0.\\ {\varphi }_{net}\text{will correspond to surface}\\ \text{which are intersected by the field lines.}\end{array}$