Consider a solid sphere of radius r and mass m which has a charge q distributed uniformly over its volume. The sphere is rotated about a diameter with an angular speed ω. Show that the magnetic moment μ and the angular momentum ℓ of the sphere are related as

A rectangular coil of 100 turns has length 5 cm and width 4 cm. It is placed with its plane parallel to a uniform magnetic field and a current of 2A is sent through the coil. Find the magnitude of the magnetic field B, if the torque acting on the coil is 0.2 N m^–1.

A circular coil of radius 2.0 cm ahs 500 turns in it and carries a current of 1.0 A. Its axis makes an angle of 30° with the uniform magnetic field of magnitude 0.40 T that exist in the space. Find the torque acting on the coil.

A rectangular loop of sides 20 cm and 10 cm carries a current of 5.0 A. A uniform magnetic field of magnitude 0.20 T exists parallel to the longer side of the loop.

(a) What is the force acting on the loop?

(b) What is the torque acting on the loop?

A circular loop carrying a current i has wire of total length L. A uniform magnetic field B exists parallel to the plane of the loop.

(a) Find the torque on the loop.

(b) If the same length of the wire is used to form a square loop, what would be the torque? Which is larger?

Fe⁺ions are acceleration through a potential difference of 500 V and are injected normally into a homogeneous magnetic field B of strength 20.0 mT. Find the radius of the circular paths followed by the isotopes with mass numbers 57 and 58. Take the mass of an ion = A(1.6 × 10^–27) kg where A is the mass number.

A charged particle moves along a circle under the action of possible constant electric and magnetic fields. Which of the following are possible?

A charged particle moves in a gravity-free space without change in velocity. Which of the following is/are possible?

If a charged particle at rest experiences no electromagnetic force,

If a charged particle goes unaccelerated in a region containing electric and magnetic fields.