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Question
A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in the Figure. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)
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Solution
Based on the illustration, we can assume that the given square represents one side of a cube with an edge length of 10 cm.
The cube encloses the +10 µC charge because it is located 5 cm above the square’s center. According to Gauss’s theorem, cube-linked electric flow is:
Φ = `q/ε_0`
= `(10 xx 10^-6)/(8.85 xx 10^-12)`
= 1.13 × 106 N m2 C−1
Since the charge is at the centre, the flux is equally distributed through the 6 faces of the cube.
Therefore, flux through one square face:
Φsq = `Φ/6`
= `1.13/6 xx 10^6`
= 0.188 × 106 N m2 C−1
or Φsq = 1.9 × 105 N m2 C−1
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