Motional EMF: Sliding Rods, Rotating Conductors, and Generators

All flashcards

Magnetic flux

For a uniform field through a flat surface, $\Phi_m = BA\cos\theta$, where $\theta$ is measured from the surface normal.

Motional emf

An induced potential difference associated with conductor motion in a magnetic field; in the standard sliding-rod geometry, $|\varepsilon|=B\ell v$.

Lenz’s law

The induced current produces a magnetic field that opposes the change in flux causing the current.

Rotating-rod emf

For a rod of length $r$ rotating at angular speed $\omega$ in the stated geometry, $|\varepsilon|=Br^2\omega/2$.

Peak emf of a rotating coil

For an $N$-turn coil of area $A$ rotating at angular speed $\omega$ in field $B$, $\varepsilon_0=NBA\omega$.

Quiz questions

1. For a uniform magnetic field through a flat surface, which quantities determine magnetic flux?Answer: Field strength, surface area, and the angle between the field and surface normal.
2. A rod of length $\ell$ moves at speed $v$ in the standard perpendicular-field sliding-rod arrangement. What is the emf magnitude?Answer: $B\ell v$
3. In a sliding-rod circuit with a resistor, what happens to the mechanical input power when the rod moves at constant speed?Answer: It equals the electrical power dissipated as heat in the resistor.
4. What physical process produces an alternating emf in a rotating-coil generator?Answer: Mechanical rotation changes the magnetic flux through the coil.
5. Why is a complete circuit needed for sustained current in an electrodynamic tether?Answer: It provides a continuous path for charge to flow.