JEE MainPhysicsElectrostatics
A thin non-conducting circular disc of radius R has a uniform surface charge density . It is placed such that its center exactly coincides with the midpoint of an edge of a cube of side length a (where a > 2R ). The plane of the disc is perpendicular to that edge. The total electric flux through all the faces of the cube is (Take ₀ as the permittivity of free space)
Options
- AR^2 4 ₀
- BR^2 2 ₀
- CR^2 8 ₀
- DR^2 ₀
Correct answer
A. R^2 4 ₀
Step-by-step solution
The total charge on the disc is q = R^2 . The edge of a cube is formed by the intersection of two faces at an angle of 90^ . Since the disc is centered on the edge and its plane is perpendicular to the edge, exactly a 90^ sector of the disc lies inside the volume of the cube. Therefore, the fraction of the disc's area (and hence its charge) enclosed by the cube is 90^ 360^ = 1 4 . Enclosed charge, q_ en = R^2 4 . By Gauss's Law, the total electric flux through the cube is = q_ en ₀ = R^2 4 ₀ . Answer: R^2 4 ₀