A non conducting sphere of radius R charged uniformly with surface density `sigma` rotates with an angular velocity `omega` about the axis passing through its centre. Find the magnetic field at the centre of the sphere.

Radius of gyration of a ring of radius R about an axis passing through its centre and perpendicular to its plane is

Two particles , each of mass m and charge q , are kept at the two ends of a light rod of length 2l and is rotated with a uniform angular velocity about the vertical axis passing through the centre of the rod . Determine the ratio of the magnetic moment and the angular momentum of the combination with respect to the centre of the rod .

A uniform metallic circurlar disc of mass M and radius R, mounted on frictionless bearings, is rotating at an angular speed omega about an axis passing through its centre and perpendicular to its plane. The temperature of the disc is then increased by Deltat . If alpha is the coefficient of linear expansion of the metal.

Two particles, each of mass m and charge q are attached to the two ends of a light rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through ts centre. Find the ratio of the magnetic moment of the system and its angular momentum about the axis through the centre of the rod.

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are