Question
A disc of radius $$\frac{a}{4}$$ having a uniformly distributed charge $$6C$$ is placed in the $$x-y$$ plane with its centre at $$\left( { - \frac{a}{2},0,0} \right).$$ A rod of length $$a$$ carrying a uniformly distributed cherge $$8C$$ is placed on the $$x$$-axis from $$x = \frac{a}{4}$$ to $$x = \frac{{5a}}{4}.$$ Two point charges $$-7C$$ and $$3C$$ are placed at $$\left( {\frac{a}{4}, - \frac{a}{4},0} \right)$$ and $$\left( { - \frac{{3a}}{4},\frac{{3a}}{4},0} \right),$$ respectively. Consider a cubical surface formed by six surfaces $$x = \pm \frac{a}{2},y = \pm \frac{a}{2},z = \pm \frac{a}{2}.$$ The electric flux through this cubical surface is
A disc of radius $$\frac{a}{4}$$ having a uniformly distributed charge $$6C$$ is placed in the $$x-y$$ plane with its centre at $$\left( { - \frac{a}{2},0,0} \right).$$ A rod of length $$a$$ carrying a uniformly distributed cherge $$8C$$ is placed on the $$x$$-axis from $$x = \frac{a}{4}$$ to $$x = \frac{{5a}}{4}.$$ Two point charges $$-7C$$ and $$3C$$ are placed at $$\left( {\frac{a}{4}, - \frac{a}{4},0} \right)$$ and $$\left( { - \frac{{3a}}{4},\frac{{3a}}{4},0} \right),$$ respectively. Consider a cubical surface formed by six surfaces $$x = \pm \frac{a}{2},y = \pm \frac{a}{2},z = \pm \frac{a}{2}.$$ The electric flux through this cubical surface is
A.
$$\frac{{ - 2C}}{{{\varepsilon _0}}}$$
B.
$$\frac{{ 2C}}{{{\varepsilon _0}}}$$
C.
$$\frac{{10C}}{{{\varepsilon _0}}}$$
D.
$$\frac{{12C}}{{{\varepsilon _0}}}$$
Answer :
$$\frac{{ - 2C}}{{{\varepsilon _0}}}$$
Solution :
From the figure it is clear that the charge enclosed in the cubical surface is $$3C + 2C - 7C = - 2C.$$ Therefore the electric flux through the cube is
$$\phi = \frac{{{q_{{\text{in}}}}}}{{{\varepsilon _0}}} = \frac{{ - 2C}}{{{\varepsilon _0}}}$$
From the figure it is clear that the charge enclosed in the cubical surface is $$3C + 2C - 7C = - 2C.$$ Therefore the electric flux through the cube is
$$\phi = \frac{{{q_{{\text{in}}}}}}{{{\varepsilon _0}}} = \frac{{ - 2C}}{{{\varepsilon _0}}}$$
