Moving Charges and Magnetism Test - 10

The magnetic moment associated with a coil carrying current is given by the product of its area and the current through it.
M = niA

The potential energy of a magnetic dipole of moment m placed in a magnetic field is U = −mB cosθ
When the magnet is aligned in the direction of the field, and the initial potential energy U_t = -mB
When the magnet is aligned opposite to the direction of the field θ =180
its potential energy is U_f = mB
Work done in rotating the magnet is equal to the change in its potential energy.
W = U_f - U_i = mB - (-mB)
2mB = 2 × 2 × 5 × 10⁻³
= 2 × 10⁻²J

The potential energy of a magnetic dipole of moment m placed in a magnetic field is U  = − mBcosθ.
When the magnet is aligned in the direction of the field, and the initial potential energy U_t = -mB
When the magnet is placed perpendicular to the direction of the field, θ = 90
its potential energy is U_f = 0.
Work done in rotating the magnet is equal to the change in its potential energy.
W = U_f − U_i = 0 − (mB) = mB =2 × 0.1 = 0.2J

A solenoid carrying current produces a magnetic field very similar to that of bar magnet. The magnetic field lines emerge from the ends of a solenoid and the number of field lines near its perpendicular bisector is almost equal to zero. A circular coil produces field along its axis. A straight conductor produces a magnetic field that can be represented by concentric circles. A toroid is a solenoid that has collapsed on itself. The field in a toroid is confined to the ring like region bounded by the toroid.

Lorentz force is given by F = Bqv sinθ
When the proton enters the magnetic field parallel to the direction of the lines of force, θ = 0.
Therefore F = 0