Question

Charge is uniformly distributed in a space. The net flux passing through the surface of an imaginary cube of side''a'' in the space is $\varphi$ and in the space it is 0. The net flux passing through the surface of an imaginary sphere of radius ''a'' in the space will be:

• A. $\varphi$
• B. $\frac{3}{4\pi }\varphi$
• C. $\frac{2\pi }{3}\varphi$
• D. $\frac{4\pi }{3}\varphi$

Answer 1

Answer: (C)

$\frac{2\pi }{3}\varphi$

External flux of a surface is given by : E.ds.

Since, the flux through the cube would be $E\times 6a^2=\varphi \Rightarrow E=\frac{\varphi }{6a^2}$

therefore for a sphere, the flux would be $E.\times 4\pi a^2$

which is equal to ${\varphi }_{sphere}=\frac{2\pi }{3}\varphi$