PHYS 2112 Ch 13 – Electromagnetic Induction

Motional emf

ℰ = BLv — emf from a conductor of length L moving with speed v perpendicular to B

When is there NO motional emf in a moving rod?

When it moves parallel to B (v × B = 0)

Magnetic flux

Φ_B = BA cos θ (θ between B and the surface normal); generally Φ_B = ∫B·dA

Unit of magnetic flux

Weber (Wb) = 1 T·m²

Faraday's law

ℰ = −N dΦ_B/dt — induced emf equals the rate of change of magnetic flux

Three ways to change flux

Change B, change area A, or change angle θ (rotate the loop)

Lenz's law

The induced current flows so its magnetic field OPPOSES THE CHANGE in flux (not the flux itself)

Lenz's law: flux increasing

Induced field points OPPOSITE to the original field

Lenz's law: flux decreasing

Induced field points in the SAME direction as the original field

Lenz's law steps

1) Find direction of original flux and whether it's increasing/decreasing 2) Find the opposing induced flux 3) Use RHR to get current direction

Electromagnetic induction

Inducing an emf by moving a magnet relative to a coil (or coil relative to a magnet)

Electric generator principle

A coil rotating in a magnetic field has changing flux → induced emf (Faraday's law)

Moving bar on rails with resistor — direction of magnetic force on bar

Opposes the motion (magnetic braking, consistent with Lenz's law)