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Question
What will be the total flux through the faces of the cube (figure) with side of length a if a charge q is placed at
- A: a corner of the cube.
- B: mid-point of an edge of the cube.
- C: centre of a face of the cube.
- D: mid-point of B and C.
Solution
a. Use of symmetry consideration may be useful in problems of flux calculation. We can imagine the charged particle is placed at the centre of a cube of side 2a. We can observe that the charge is being shared equally by 8 cubes. Therefore, total flux through the faces of the given cube = `q/(8ε_0)`
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| (A) | (B) |
b. If the charge q is placed at B, middle point of an edge of the cube, it is shared equally by 4 cubes. Therefore, total flux through the faces of the given cube = `q/(4ε_0)`
c. If the charge q is placed at C, the centre of a face of the cube, it is being shared equally by 2 cubes. Therefore, total flux through the faces of the given cube = `q/(2ε_0)`
d. Finally, if charge q is placed at D, the mid-point of B and C, it is being shared equally by 2 cubes. Therefore, total flux through the faces of the
given cube = `q/(2ε_0)`
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