First slide

Gauss's law and its applications

Question

A linear charge having linear charge density $λ$ penetrates a cube diagonally and then it penetrates a sphere diametrically as shown. What will be the ratio of flux coming out of cube and sphere

Moderate

A

$\frac{1}{2}$
B

$\frac{2}{\sqrt{3}}$
C

$\frac{\sqrt{3}}{2}$
D

$\frac{1}{1}$

Solution

Flux coming out of the cube
$ϕ_{1} = \frac{λ \cdot a \sqrt{3}}{ε_{0}} . . . . . . . . (i)$
and from sphere
$ϕ_{2} = \frac{λ \cdot 2 a}{ε_{0}} . . . . . . . . . (i i)$
$∴ \frac{ϕ_{1}}{ϕ_{2}} = \frac{\sqrt{3}}{2}$

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