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  4. A linear charge having linear charge density λ, penetrates a cube diagonally and then it penetrates a sphere diametrically as shown. The ratio of flux coming out of the cube and the sphere is (√x/y). Find (x y).

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Q. A linear charge having linear charge density $\lambda$, penetrates a cube diagonally and then it penetrates a sphere diametrically as shown. The ratio of flux coming out of the cube and the sphere is $\frac{\sqrt{x}}{y}$. Find $(x y)$.Physics Question Image

Electric Charges and Fields

Solution:

Flux coming out of the cube, $\phi_{1}=\frac{\lambda \cdot a \sqrt{3}}{\varepsilon_{0}}$...(i)
Flux coming out of the sphere, $\phi_{2}=\frac{\lambda \cdot 2 a}{\varepsilon_{0}}$...(ii)
$\therefore \frac{\phi_{1}}{\phi_{2}}=\frac{\sqrt{3}}{2}$