12- Magnetic Dipole moment

What is the expression for current in a wire?

• n = the number density of electrons

• A = the cross sectional area of the wire

• v= average drift velocity

What is the expression for the total Lorentz force acting on electrons in a wire?

• I= current

• L= Length of the section of wire

• B= magnetic field strength (magnetic flux density)

What happens to the electrons in the presence of a perpendicular magnetic field?

The magnetic force pushes them in a direction perpendicular to both the current and the field.

Why does the wire move in a magnetic field if unconstrained?

The force on the electrons is transmitted to the wire itself.

What is the angle between velocity and magnetic field in equation F=BIL?

What is the torque on a rectangular current loop in a magnetic field?

How is the magnetic dipole moment m of a current loop defined?

A is the area vector, with magnitude equal to the loop's area and direction given by the right-hand rule.

What is the analogy between a magnetic dipole in a field and an electric dipole?

The torque equations are similar:

What is the far-field dependence of a magnetic dipole’s field?

This is similar to an electric dipole’s field.

What is the formula for the magnetic potential energy of a dipole in a magnetic field?

What is the analogy between electric and magnetic dipole potential energy?

When does a magnetic dipole have minimum potential energy?

When m is aligned with B (lowest energy state).

What is the energy difference between the highest and lowest energy states of a magnetic dipole?

2mB

What must be done to rotate a magnetic dipole against the field?

Work must be done by an external force to change its orientation.

What is the basic principle behind a d.c. motor?

A current-carrying loop in a magnetic field experiences a torque, causing it to rotate.

Why does a simple current loop in a magnetic field not make a good motor?

The torque reverses after θ=0, causing oscillation instead of continuous rotation.

How does a split-ring commutator help in a d.c. motor?

It reverses the current at θ=0, ensuring the torque always acts in the same direction.

What role do brush contacts play in a d.c. motor?

They provide a continuous electrical connection to the rotating commutator.

Why does a basic d.c. motor run in a jerky manner?

The current only reverses at certain points, causing brief pauses in the torque.

How is the performance of a d.c. motor improved?

By using multiple coils at different orientations and a multi-segment commutator for smoother torque.