A charge Q is distributed uniformly over a rod of length l . A hypothetical cube of edge l is positioned such that its centre coincides with one end of the rod. Determine the minimum possible flux of the electric field through the entire surface of the cube.

Step-by-step solution

By Gauss's law, the electric flux through the entire surface of the cube is given by = q_ enclosed ₀ . To minimize the flux, the charge enclosed by the cube must be minimized. The rod has a uniform linear charge density = Q l . The enclosed charge is q_ enclosed = l_ enclosed , where l_ enclosed is the length of the rod inside the cube. One end of the rod is fixed at the centre of the cube. To minimize the length of the rod inside the cube, the rod must be oriented along the shortest path from the centre to the sur