What will be the total flux through the faces of a cube with side 'a' if a charge is placed at 'B' mid point of an edge of the cube (shown in figure)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{q}{4\varepsilon_0} \)
By Gauss’s law the total flux through a closed surface enclosing a charge q is \( q/\varepsilon_0 \). A charge at the middle of an edge is not inside the cube. It is shared by four identical cubes that meet along that edge, and by symmetry each cube gets an equal part of the total flux.
\( \displaystyle \phi = \frac{1}{4}\cdot\frac{q}{\varepsilon_0} = \frac{q}{4\varepsilon_0} \)
Shortcut: Count how many equal cubes would surround the charge: 8 for a corner, 4 for the middle of an edge, 2 for the centre of a face, 1 when it is at the centre. The flux through the given cube is \( q/\varepsilon_0 \) divided by that number.
Note: The same question was also asked in CUET (UG) 2023 on 14-06-2023 (Slot 2).
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 – …
