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A positively charged particle with specific charge sigma leaves the origin with a velocity u directed along positive x direction. The entire space has a uniform electric field (E) and magnetic field (B) directed along the positive y direction. Find the angle that the velocity of the particle makes with y direction at the instant it crosses the y axis for n^(th) time.

A long cylindrical shell carries positive surface charge sigma in the upper half and negative surface charge -sigma in the lower half. The electric field lines around the cylinder will look like figure given in:(figures are schematic and not drawn to scale)

Find the position of centre of mass of the uniform lamina shown in figure. If the mass density of the lamina is sigma .

Suppose the surface charge density over a sphere of radius R depends on a polar angle theta as sigma = sigma_(0)cos theta , where sigma_(0) is a positive constant. Show that such a charge distribution can be represented ~s a result ofa small relative shift of two uniformly · charged balls of radius R whose charges are equal in magnitude and opposite in sign. Resorting to this representation, find the electric field strength vector inside the given sphere. [(sigma_(0))/(3in_(0))]

Two infinite parallel,non- conducting sheets carry equal positive charge density sigma ,One is placed on the other at distance x=a Take potential V=0 at x=0 then

An infinite plane sheet of positive charge has surface charge density sigma . A metallic ball of mass m and charge +Q is attached to a thred and is tied to a point A on the sheet PQ . The angle theta made by the string with plane sheet is in equilibrium is