A disc of radius having a uniformly distributed charge 6C is placed in the plane with its centre at . A rod of length carrying a uniformly distributed charge 8C is placed on the -axis from to . Two point charges and 3C are placed at and , respective

Question

A disc of radius $a / 4$ having a uniformly distributed charge 6C is placed in the $x - y$ plane with its centre at $(- a / 2, 0, 0)$ . A rod of length $a$ carrying a uniformly distributed charge 8C is placed on the $x$ -axis from $x = a / 4$ to $x = 5 a / 4$ . Two point charges $- 7 C$ and 3C are placed at $(a / 4, - a / 4, 0)$ and $(- 3 a / 4, 3 a / 4, 0)$ , 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 [2009]

Smart Achievers · Accepted Answer

(1)

From the figure, total charge enclosed in the cubical surface is $q_{in} = 3 C + 2 C - 7 C = - 2 C$

According to Gauss's theorem, the electric flux through the cube is

$ϕ = \frac{q_{in}}{ε_{0}}$ $= \frac{- 2 C}{ε_{0}}$

Solution

1 $- \frac{2 C}{ε_{0}}$

2 $\frac{2 C}{ε_{0}}$

3 $\frac{10 C}{ε_{0}}$

4 $\frac{12 C}{ε_{0}}$

Ans.
(1)

From the figure, total charge enclosed in the cubical surface is $q_{in} = 3 C + 2 C - 7 C = - 2 C$

According to Gauss's theorem, the electric flux through the cube is

$ϕ = \frac{q_{in}}{ε_{0}}$ $= \frac{- 2 C}{ε_{0}}$

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Solution

1 -2Cε0

2 2Cε0

3 10Cε0

4 12Cε0