Consider a solid sphere of radius r and mass m having a charge q distributed uniformly throughout its volume. The sphere rotates about a diameter with an angular speed . The relationship between the magnetic moment and the angular momentum l of the sphere is given by

Step-by-step solution

For a rigid body having uniform charge and mass distribution, the ratio of charge to mass for any elemental volume is constant. Let the uniform charge density be _q = q V and uniform mass density be _m = m V . Consider an elemental volume dV rotating at a perpendicular distance x from the axis of rotation with angular speed . The charge of the element is dq = _q dV and its mass is dm = _m dV . The magnetic moment of this rotating element is d = 1 2 dq x^2 . The angular momentum of the element is dl = dm x^2 . Takin