22.3 Magnetic Normal MAGNETIC FLUX vector

The magnetic flux is proportional to the number of field lines that passthrough a surface.

Directional boundary path. Circulation sense related to normal vector by RHR-2 Unit: T·m2 = “” (Wb) Φ B = BAcosφ

FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION

The average emf induced in a coil of N loops is Review:  Φ − Φo  ∆Φ E = −N  = −N SI Unit of Induced  t − to  ∆t Emf: volt (V) 1 22.5 Lenz’s Law LENZ’S LAW (gives you the direction of the induced current)

The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced opposes the original flux change.

Change in flux  induced emf  induced current  induced B field opposes change in flux

Reasoning Strategy

1. Determine whether the magnetic flux that penetrates the coil is increasing or decreasing.

2. Find what the direction of the induced magnetic field must be so that it can oppose the change in flux by adding or subtracting from the original field.

3. Use RHR-2 to determine the direction of the induced current from the induced field in step 2.

2 22.5 Lenz’s Law Case 2: The Emf Produced by a Moving A permanent magnet is approaching a loop of wire. The external circuit consists of a resistance. Find the direction of the induced current and the polarity of the induced emf.

Answer:

1. As the magnet moves to the right, the field lines at the loop get closer together  magnetic flux to the right is increasing

2. Induced magnetic field must point to the left to oppose the increase.

3. The induced current is then given by RHR-2 as shown in figure (b)

3 22.5 Lenz’s Law Case 2: The Emf Produced by a Moving Coil.

There is a constant magnetic field directed into the page in the shaded region. The field is zero outside the shaded region.

A Coil slides through the region. For each of the five positions, determine whether an induced current exists or not. If it does, find its direction.

1. No field  no flux change  no current

2. Flux is increassing into the page  induced magnetic field points out of page  induced current in the CCW direction

3. Flux is negative, but not changing  no induced current

4. Flux is is decreasing into the page induced magnetic field points into the page  induced current in the CW

5. Same as 1: no induced current.

4 22.7 The HOW AN AC GENERATOR PRODUCES EMF v ω = The magnetic Simple external r Device being force on all parts contacts: powered Unlike in a DC Zooming in of the loop are motor (Ch. 21), the on the loop vertical by RHR-1 brushes DO NOT switch the contacts Vertical force back-and-forth produces NO emf on the horizontal segments

EMF by induction On each vertical segment, the magnetic forces generate motional emf given by E = (vB sinθ )L = BLv sinθ

Induced current flows up on the segment in front and down on the back 1 r But v = rω = ω ⋅ 2 W

1 1 Mechanical E ↑,↓ = 2 BLWω sinθ = 2 BAω sinθ power input 5 22.7 The Electric Generator θ = ω t NOTE: ω ≠ W v ω = W = wdith of the coil r ω = angular speed of rotation of the loop/coil − 1 E ↑,↓ = 2 BAω sinθ + + 1 = 2 BAω sinω t (is equivalent≡ to) − For each loop in a coil we have two of these terms

ELOOP = BAω sinθ Emf induced in a rotating planar coil of N turns

E = NABω sinω t ω = 2π f E(t) or or E(t) = E0 sinω t V (t) = V0 sinω t V (t)

Peak emf / source

E0 = V0 = NBAω 6