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Question
A charge Q is uniformly distributed over a rod of length l. Consider a hypothetical cube of edge l with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.
Solution
Given:
Total charge on the rod = Q
The length of the rod = edge of the hypothetical cube = l
Portion of the rod lying inside the cube, `"x" ="l"/2`
Linear charge density for the rod = `"Q"/"l"`
Using Gauss's theorem, flux through the hypothetical cube,
Ø = (Qin/∈0) , where Qin = charge enclosed inside the cube
Here, charge per unit length of the rod = `"Q"/"l"`
Charge enclosed, `Q_("in") = "Q"/"l" xx "l"/2 = "Q"/2`
Therefore , Ø = ` ("Q"/2)/∈_0 = "Q"/(2∈_0)`
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