A cubical region of side a has its centre at the origin. It...

A cubical region of side

a

has its centre at the origin. It encloses three fixed point charges,

-q

(0,-a / 4,0),+3 q

(0,0,0)

and

-q

(0,+a / 4,0)

. Choose the correct options(s) 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

Options

AThe net electric flux crossing the plane $x=+a / 2$ is equal to the net electric flux crossing the plane $x=-$ $a / 2$
BThe net electric flux crossing the plane $y=+a / 2$ is more than the net electric flux crossing the plane $y=-a / 2$ .
CThe net electric flux crossing the entire region is $\frac{q}{\varepsilon_{0}}$
DThe net electric flux crossing the plane $z=+a / 2$ is equal to the net electric flux crossing the plane $x=+a / 2$ .

Correct answer

A. The net electric flux crossing the plane $x=+a / 2$ is equal to the net electric flux crossing the plane $x=-$ $a / 2$

Step-by-step 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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