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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?
Solution
The sphere of radius 4a is enclosed within Only the negative charge Q1 = −4Q. Outside the sphere is the positive charge Q2 = +2Q, which is placed at a distance of 5a from the origin. Only a part of the electric flux lines originating at Q2 through the sphere and completely exit at other points. As a result, the electric flux through the sphere is solely caused by Q1.
Therefore, the net electric flux through the sphere `= "Q"_1/epsilon_0 = (-4"Q")/epsilon_0`.
Because the sphere is not centred on Q1, the minus sign indicates that the flux is directed into the sphere but not radially.
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