Verified Solution • 2025–26 Session moderate

QNEET-2023-Ph-344: NEET 2023 Physics - Class 12 NEET-2023-Ph-344 Solution: A charge \(Q C\) is placed at the centre of a cube. The flux…

A charge QμCQ \mu C is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit): Q×10−63ϵ0\frac{Q \times 10^{-6}}{3\epsilon_0} 2Q×10−36ϵ0\frac{2Q \times 10^{-3}}{6\epsilon_0} Q×10−36ϵ0\frac{Q \times 10^{-3}}{6\epsilon_0} Q×10−66ϵ0\frac{Q \times 10^{-6}}{6\epsilon_0}

Multiple Choice Options

  • A Qϵ0×10−6\frac{Q}{\epsilon_0} \times 10^{-6} _ 0 _ Q _ _ 1 0 _ 6
  • B 2Q3ϵ0×10−3\frac{2 \mathrm{Q}}{3 \epsilon_0} \times 10^{-3} 3 _ 0 _ 2 Q _ _ 1 0 _ 3
  • C Q6ϵ0×10−3\frac{\mathrm{Q}}{6 \epsilon_0} \times 10^{-3} 6 _ 0 _ Q _ _ 1 0 _ 3
  • D Q6ϵ0×10−6\frac{\mathrm{Q}}{6 \epsilon_0} \times 10^{-6} 6 _ 0 _ Q _ _ 1 0 _ 6

Step-by-Step Verified Solution

The Gaussian surface for the charge placed at the center of the cube will spread out equally through all sides of the cube. According to Gauss's Law, electric flux _ through a closed surface is equal to the charge enclosed Q divided by the permittivity of free space _ 0 : _ total = Q _ 0 Given that the cube has 6 faces, and due to symmetry, the flux through each face will be equal, the flux through any one face _ face is: _ face = _ total 6 = Q 6 _ 0 Since the charge is given in microcoulombs ( _ C ), we need to convert it to coulombs by multiplying with 10 _ 6 : _ face = Q _ 10 _ 6 6 _ 0 This matches option D, which means the correct flux through one face of the cube given a charge Q microcoulombs at the center is Q 6 _ 0 _ 10 _ 6 .

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