Question

Two charges of magnitudes -4Q and +2Q are located at points (2a, 0) and (5a, 0) respectively. What is the electric flux due to these charges through a sphere of radius 4a with its centre at the origin?

Answer 1

The sphere of radius 4a encloses only the negative charge Q₁ = -4Q. The positive charge Q₂ = +2Q being located at a distance of 5a from the origin is outside the sphere. Only a part of the electric flux lines originating at Q₂ enters the sphere and exits entirely at other points. Hence, the electric flux through the sphere is only due to Q₁.
Therefore, the net electric flux through the sphere = \(\frac{Q_{1}}{\varepsilon_{0}}=\frac{-4 Q}{\varepsilon_{0}}\) . The minus sign shows that the flux is directed into the sphere, but not radially since the sphere is not centred on Q₁.