(a) Using Gauss law, derive expression for electric field due to a spherical shell of uniform charge distribution σ and radius R at a point lying at a distance x from the centre of shell, such that
(i) 0 < x < R, and
(ii) x > R.
(b) An electric field is uniform and acts along + x direction in the region of positive x. It is also uniform with the same magnitude but acts in – x direction in the region of negative x. The value of the field is E = 200 N/C for x > 0 and E = – 200 N/C for x < 0. A right circular cylinder of length 20 cm and radius 5 cm has its centre at the origin and its axis along the x-axis so that one flat face is at x = + 10 cm and the other is at x = – 10 cm.
Find :
(i) The net outward flux through the cylinder.
(ii) The net charge present inside the cylinder.
OR
(a) Find the expression for the potential energy of a system of two point charges q1 and q2 located at r1 & r2, respectively in an external electric field E .
(b) Draw equipotential surfaces due to an isolated point charge (– q) and depict the electric field lines.
(c) Three point charges +1μC, –1μC and +2μC are initially infinite distance apart. Calculate the work done in assembling these charges at the vertices of an equilateral triangle of side 10 cm.
