A circle of radius 'a' has charge density given by `lambda= lambda_(0)cos^(2)theta` on its circumference. What will be the total charge on the circle ?

A circle of radius a has charge density given by lambda=lambda_(0)cos^(2)theta on its circumference, where lambda_(0) is a positive constant and theta is the angular position of a point on the circle with respect to some reference line. The potential at the centre of the circle is

A thin non-conducting ring of radius R has a linear charge density lambda=lambda_(0) cos theta , where theta is measured as shown. The total electric dipole moment of the charge distribution is

Charge on the ring is given as lambda=lambda_(0)cos theta C/m .Find dipole moment of the ring

The linear charge density of a uniform semicircular wire varies with theta shown in the figure as lambda=lambda_(0)costheta if R is the radius of the loop ,of the charge on the wire is

A non conducting ring of radius R_(1) is charged such that the linear charge density is lambda_(1)cos^(2)theta where theta is the polar angle. If the radius is increased to R_(2) keeping the charge constant, the linear charge density is changed to lambda_(2)cos^(2)theta . The relation connecting R_(1) , R_(2)lambda_(1) and lambda_(2) will be

A thin non-conducting ring or radius a has a linear charge density lambda = lambda_(0) sin phi . A uniform electric field E_(0) hat(i) + E_(0) hat(j) exist in the region . .Net torque acting on ring is given as :

A plastic rod has been formed into a circle of radius R. It has a positive charge +Q uniformly distributed along one-quarter of its circumference and a negative charge of -6Q uniformly distributed along the rest of the circumference (figure). With V = 0 at infinity, what is the electric potential -6Q (a) at the centre C of the circle and (b) at point P, which is on the central axis of the circle at distance z from the centre?