A cubical region of side $a$ has its centre at the origin. It encloses three fixed point charges, $-q$ at…
A cubical region of side $a$ has its centre at the origin. It encloses three fixed point charges, $-q$ at $(0,-a / 4,0),+3 q$ at $(0,0,0)$ and $-q$ at $(0,+a / 4,0)$. Choose the correct options(s)
The net electric flux crossing the plane $x=+a / 2$ is equal to the net electric flux crossing the plane $x=-$ $a / 2$
The net electric flux crossing the plane $y=+a / 2$ is more than the net electric flux crossing the plane $y=-a / 2$.
The net electric flux crossing the entire region is $\frac{q}{\varepsilon_{0}}$
The net electric flux crossing the plane $z=+a / 2$ is equal to the net electric flux crossing the plane $x=+a / 2$.
Solution
Due to symmetry, the net electric flux passing through $x=+\frac{a}{2}$, $x=-\frac{a}{2}, z=+\frac{a}{2}$ is same
According to Gauss's theorem, net electric flux net electric flux crossing through any closed surface $\phi=\frac{q_{\text {in }}}{\varepsilon_{0}}=$ $\frac{-q+3 q-q}{\varepsilon_{0}}=\frac{q}{\varepsilon_{0}}$.
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