Two coaxial rings, eacg of radius R, made of thin wire are separated by a small distabce `l(l lt lt R)` and carry the charges `q` and `-q`. Find the electric field potential and strength at the axis of the system as a function of the x coordinate (see figure). Investigate these functions at `|x| gt gt R`

A very thin round plate of radius R carrying a uniform surface charge density sigma is located in vacumm. Find the electric field potentail and strength along the plate's axis as a function of a distance l from its centre. Investigation the obtained expression of l rarr 0 and l gt gt R .

A thin nonconducting ring of radius R has a linear charge density lambda = lambda_(0) cos varphi , where lambda_(0) is a constant , phi is the azimuthal angle. Find the magnitude of the electric field strength (a) at the centre of the ring , (b) on the axis of the ring as a function of the distance x from its centre. Investegation the obtained function at x gt gt R .

A thin nonconducting ring of radius R has a linear charge density lambda = lambda_(0) cos varphi , where lambda_(0) is a constant , phi is the azimutahl angle. Find the magnitude of the electric field strength (a) at the centre of the ring , (b) on the axis of the ring as a function of the distance x from its centre. Investegation the obtained function at x gt gt R .

A thin wire of radius ..r.. carries a charge q. Find the magnitude of the electric field strength on the axis of the ring as a function of distance L from the centre. Find the same for L gt gt r Find maximum field strength and the corresponding distance L.

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) .

A charge Q is uniformly on a ring of radius R . Find the electric potential on the axis of ring at distance x from the centre of the ring. Sketch variation of potential with respect to x .