Question

Two charges of magnitudes -2 Q and + Q are located at points (a, 0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius 3a with its centre at the origin? [AI 2013]

Answer 1

Given,

Two charges of magnitude -2Q and +Q are located at points (a, 0) and (4a, 0) respectively.

To find,

the electric flux due to these charge through a sphere of 3a with its centre at the origin.

we know from Gauss law, electric flux is the ratio of charge enclosed the Gaussian surface to the permittivity of medium.

i.e., Φ = Q_in/∈0

see figure, it is clear that charge located at (4a, 0) i.e., +Q presents outside the Gaussian surface but charge located at (a,0) contains inside the Gaussian surface.

charge enclosed = Q_in = -2Q

so electric flux, Φ =-2Q/∈0