Current-Loop Torque, Magnetic Dipole Energy, and Motor Rotation

All flashcards

What is the magnetic force on a straight wire segment?

It is $\vec{F}=I\vec{\ell}\times\vec{B}$, where $I$ is current, $\vec{\ell}$ points along the current, and $\vec{B}$ is the magnetic field.

Why is the net force on a closed loop zero in a uniform field?

Forces on opposite current-carrying segments are equal in magnitude and opposite in direction, so they cancel when added as vectors.

Does zero net force mean a loop cannot rotate?

No. Forces that cancel in total can act at different positions and create a nonzero torque.

What determines the torque on a current loop in a magnetic field?

The vector relation is $\vec{\tau}=\vec{\mu}\times\vec{B}$, where $\vec{\mu}$ is the loop's magnetic dipole moment.

What is the magnetic dipole moment of a coil?

It is a vector describing the magnetic strength and orientation of a current loop: $\vec{\mu}=NIA\hat{\mathbf{n}}$, where $N$ is turns, $I$ is current, $A$ is area, and $\hat{\mathbf{n}}$ is normal to the loop.

Quiz questions

1. What equation gives the magnetic force on a straight current-carrying wire segment?Answer: $\vec{F}=I\vec{\ell}\times\vec{B}$
2. How can the direction of a current loop's magnetic dipole moment be found?Answer: Curl the right-hand fingers with the conventional current; the thumb points along the moment.
3. What is the net magnetic force on a closed current loop of any planar shape in a uniform magnetic field?Answer: Zero
4. How can a loop have zero net force but a nonzero torque?Answer: Equal and opposite forces can act along different lines of action, creating a turning effect.
5. What is the magnetic dipole moment of a coil with $N$ turns, current $I$, and area $A$?Answer: $\vec{\mu}=NIA\hat{\mathbf{n}}$