Magnetic flux Phi_B = BA cos theta measures how much of the magnetic field passes perpendicularly through a surface area A. Faraday's law states that a changing flux induces an emf: |epsilon| = |Delta Phi_B / Delta t|. Flux can change by changing B, A, or the angle theta between B and the area vector. Lenz's law gives the direction of the induced current: it always opposes the change in flux that caused it, which is a consequence of energy conservation. For a conducting rod of length l moving at speed v perpendicular to a uniform field B, the motional emf is epsilon = Blv.
- Phi_B = BA cos theta: Magnetic flux through a flat surface of area A in a uniform field B, where theta is the angle between B and the area vector (perpendicular to the surface). Units are webers (Wb).
- Faraday's law: |epsilon| = |Delta Phi_B / Delta t|. The magnitude of the induced emf equals the rate of change of magnetic flux through the loop. For an N-turn coil, multiply by N.
- Lenz's law: The induced current flows in the direction that creates a magnetic field opposing the change in flux. If flux through a loop increases upward, the induced current creates flux downward inside the loop.
- Motional emf: epsilon = Blv for a conducting rod of length l moving at speed v perpendicular to field B. The rod acts like a battery driving current through any connected circuit.
- Induced current: I = epsilon / R, where epsilon is the induced emf from Faraday's law and R is the resistance of the circuit. Current flows only while flux is changing.
A square loop is pulled out of a region of uniform magnetic field directed into the page. Using Lenz's law, determine the direction of the induced current in the loop as it exits the field.
| What changes | Effect on flux | Induced emf present? |
|---|
| B increases | Flux increases | Yes |
| Area of loop decreases | Flux decreases | Yes |
| Loop rotates (theta changes) | Flux changes | Yes |
| B constant, A constant, theta constant | No change | No |