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A cube has a point charge q placed at one of its vertices and a point charge Q placed at the centre of one of its edges. If the total electric flux passing through the cube is 5q 8 ₀ , the ratio Q q is :

Options

  1. A1
  2. B4
  3. C2
  4. D1 2

Correct answer

C. 2

Step-by-step solution

According to Gauss's law, the total electric flux through the cube is given by = Q_ enclosed ₀ . The charge q at the vertex is shared by 8 cubes, so its contribution to the enclosed charge is q 8 . The charge Q at the edge centre is shared by 4 cubes, so its contribution to the enclosed charge is Q 4 . The total flux through the cube is: = q 8 + Q 4 ₀ Given that = 5q 8 ₀ , we can equate the two expressions: q 8 ₀ + Q 4 ₀ = 5q 8 ₀ Q 4 = 5q 8 - q 8 = 4q 8 = q 2 Q = 2q Therefore, the ratio Q q = 2 . Answer: 2

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