An infinitely long cylindrical surface density `sigma = sigma_(0) cos varphi`. Where `varphi` is the polar angle of the cylindrical coordinate system whose `z` axis coincides with the axis of the given surface. Find the magnitude and direction of the electric field strength vector on the `z` axis.

An infineltly long cylindrical surface density sigma = sigma_(0) cos varphi . Where varphi is the polar angle of the cylindrical coordinate system whose z axis coincides with the axis of the given surface. Find the magnitude and direction of the electric fiels strength vector on the z axis.

When an uncharged conducting ball of radius R is placed in an external uniform electric field, a surface charge densityh sigma = sigma_(0) cos theta is induced on the ball's surface charge (here sigma_(0) is a constant, theta is a polar angle). Find the magnitude of the resultant electric force acting on an induced charge of the same sign.

Two infinite planes sepated by a distance l carrying a uniform surface charge of densities sigma and -sigma . The planes have round coaxial holes of radius R , with l lt lt R . Taking the origin O and the x cordinates axis as shown in the figure, find the potentail of the electric field and the projection of its strength vector E_(x) on the area of the system as functions of the x cordiante. Draw the appoximate plot varphi (x) .

In a long insulating cylinder of radius R a cylindrical tunnel of radius a located at a distance b from the axis of the cylinder as shown in the figure. R R b - The solid part of the cylinder has a uniform volume charge density P. Find the magnitude and direction of the electric field inside the tunnel.

A thin straight infinitely long conducting wire having charge density lambda enclosed bya cylindrical surface of radius r and length l_(r) , its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.

An infinitely long cylinder is kept parallel to an uniform magnetic field B directed along positive z-axis. The direction of induced current as seen from the z-axis will be

An infinite cylinder of radius r with surface charge density sigma is rotated about its central axis with angular speed omega . Then the magnetic field at any point inside the cylinder is