Moving Charges & Magnetism

A long straight wire carries a current of 5 A. Find the magnetic field at a point 10 cm from the wire.

A circular coil of 100 turns and radius 10 cm carries a current of 2 A. Find the magnetic field at its centre.

A long solenoid has 1000 turns per metre and carries a current of 2 A. Find the magnetic field well inside the solenoid.

A proton (m = 1.67 × 10⁻²⁷ kg) moves at 2 × 10⁶ m/s perpendicular to a magnetic field of 0.5 T. Find the radius of its circular path.

Find the cyclotron frequency of a proton moving in a magnetic field of 1 T.

Two long parallel wires carry currents of 3 A and 5 A and are separated by 10 cm. Find the magnetic force per unit length between them.

A toroid of mean radius 20 cm has 2000 turns and carries a current of 2 A. Find the magnetic field inside its core.

A galvanometer coil has N = 50 turns, area 4 × 10⁻⁴ m², sits in a field B = 0.2 T, and has a restoring constant C = 1 × 10⁻⁶ N·m/rad. Find its current sensitivity.

An electron moves at 1 × 10⁷ m/s perpendicular to a magnetic field of 2 × 10⁻³ T. Find the magnitude of the magnetic force on it.

A 0.5 m wire carries a current of 4 A in a magnetic field of 0.3 T, making an angle of 30° with the field. Find the magnetic force on the wire.

In the first Bohr orbit of hydrogen (r ≈ 0.53 Å, v ≈ 2.18 × 10⁶ m/s), find the equivalent orbital current of the electron.

A solid cylindrical conductor of radius 4 cm carries a current of 10 A, uniformly distributed. Find the magnetic field at a point 2 cm from the axis (inside the conductor).

A square current loop of side 20 cm carries a current of 5 A. Find the magnetic field at its centre.

A rectangular coil of 20 turns and dimensions 2 cm × 3 cm carries a current of 3 A in a field of 0.25 T, with its plane parallel to the field. Find the torque on it.

A proton moves at 1 × 10⁶ m/s at 60° to a magnetic field of 0.2 T. Find the pitch of its helical path. (m = 1.67 × 10⁻²⁷ kg)

A galvanometer has current sensitivity 100 rad/A and coil resistance 100 Ω. Find its voltage sensitivity.

A wire is bent into a three-quarter circle (270°) of radius 10 cm and carries a current of 4 A. Find the magnetic field at the centre due to this arc.

In a cyclotron, a proton reaches a maximum radius of 0.4 m in a magnetic field of 1.5 T. Find its maximum kinetic energy.