Question

A cube of side $a$ is placed such that the nearest face which is parallel to the $y-z$ plane is at distance ${}^{\prime }{a}^{\prime }$ from the origin. The electric field components are $E_x=\alpha x^{1/2},E_y=E_z=0$.
The flux ${\varphi }_E$ through the cube is

• A. $\sqrt{2}\alpha a^{5/2}$
• B. $-\alpha a^{5/2}$
• C. $(\sqrt{2}-1)\alpha a^{5/2}$
• D. Zero

Answer 1

The correct option is C $(\sqrt{2}-1)\alpha a^{5/2}$

${\varphi }_1=-E_1{a}^2=-\alpha a^{1/2}{a}^2=-\alpha a^{5/2}$

and ${\varphi }_2=E_2{a}^2=\alpha (2a{)}^{1/2}{a}^2=\sqrt{2}\alpha a^{5/2}$

${\varphi }_{net}=(\sqrt{2}-1)\alpha a^{5/2}$