A point charge Q is kept at the midpoint of a face of cube of side L. The electric flux emerging from the cube is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( Q\,(2\varepsilon_0)^{-1} \)
By Gauss's law a closed surface enclosing a charge \( Q \) has a total flux \( Q/\varepsilon_0 \). A charge lying on a face is not fully enclosed by one cube, so use symmetry.
Place an identical cube against the face that carries the charge. The two cubes together form a closed box with \( Q \) inside it, so the total flux through the box is \( Q/\varepsilon_0 \). The charge sits on the middle of the shared face, so the two cubes are placed alike with respect to it, and each receives half of this flux.
\( \displaystyle \Phi = \frac{1}{2}\,\frac{Q}{\varepsilon_0} = Q\,(2\varepsilon_0)^{-1} \)
Note: This question is from the NCERT Exemplar. NTA sets numerical questions from the Exemplar too, so do not ignore it while practising numericals.
NCERT Exemplar:
Electric Charges and Fields – …
