Three charges of magnitude −2Q, −3Q and Q are located at (a, 0, 0), (3a, 0, 0) and (5a, 0, 0) respectively. What is the magnitude of electric flux due to these charges through a sphere of radius 4a with its centre at the origin?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \displaystyle\frac{5Q}{\varepsilon_0} \)
Gauss's law says that the flux through a closed surface is the net charge enclosed divided by \( \varepsilon_0 \). Charges outside the surface contribute zero net flux.
The sphere has radius 4a and is centred at the origin. The charges at distances a and 3a from the origin are inside; the charge at 5a is outside.
\( q_{\mathrm{enc}} = -2Q + (-3Q) = -5Q \)
\( \displaystyle |\Phi| = \frac{|q_{\mathrm{enc}}|}{\varepsilon_0} = \frac{5Q}{\varepsilon_0} \)