A cubical region of side has its centre at the origin. It encloses three fixed point charges, at , at and at . Choose the correct option(s). [2012]

Question

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 option(s). [2012]

Smart Achievers · Accepted Answer

(1, 3, 4)

Due to symmetry, the net electric flux passing through

$x = + \frac{a}{2}, x = - \frac{a}{2}, z = + \frac{a}{2}$ is the same.

According to Gauss's theorem, the net electric flux crossing through any closed surface $ϕ = \frac{q_{in}}{ε_{0}}$

$= \frac{- q + 3 q - q}{ε_{0}} = \frac{q}{ε_{0}}$

Solution

Q.
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 option(s). [2012]

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

2 The net electric flux crossing the plane $y = + a / 2$ is more than the net electric flux crossing the plane $y = - a / 2$ .

3 The net electric flux crossing the entire region is $\frac{q}{ε_{0}} .$

4 The net electric flux crossing the plane $z = + a / 2$ is equal to the net electric flux crossing the plane $x = + a / 2$

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Solution

Q. A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -q at (0,-a/4,0), +3q at (0,0,0) and -q at (0,+a/4,0). Choose the correct option(s). [2012]

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

2 The net electric flux crossing the plane y=+a/2 is more than the net electric flux crossing the plane y=-a/2.

3 The net electric flux crossing the entire region is qε0.

4 The net electric flux crossing the plane z=+a/2 is equal to the net electric flux crossing the plane x=+a/2