LECTURE 29INDUCED EMFInstructor: Kazumi Tolich

Lecture 292

¨ Reading chapter 23-1 & 23-2.¤ Induced emf¤ Magnetic flux¤ Faraday’s law¤ Lenz’s law

Demo: 13

¨ Faraday’s experiment: magnetic induction¨ Current is induced in the secondary circuit while the

current in the primary circuit is changing.¨ The induced current flows in opposite directions

depending on whether the magnetic field is increasing or decreasing.

¨ Changing magnetic field creates induced emf.

Induced current by a moving magnet4

¨ A coil experiences an induced current when the magnetic field passing through it varies.

¨ The direction of the induced current depends on the velocity direction of the magnet.

Magnetic flux5

¨ Magnetic flux is used in the calculation of the induced emf.

¨ Magnetic flux is the measure of the amount of magnetic field penetrating a given area.

¨ Magnetic flux is defined by

¤ B is the magnetic field that go through the surface A.

¨ The SI unit for magnetic flux is Weber, Wb (T·∙m2).

Φ = BAcosθ

Example: 16

¨ The figure shows a circular loop with a diameter d = 10 cm rotating in a uniform magnetic field of B = 0.050 T. What are the magnitudes of the flux through the loop when the angles are θ = 0°, and 60°?

Faraday’s law & Lenz’s law7

¨ Faraday’s law states: an emf, E, is induced in a conducting coil with N loops if the magnetic flux Φ through the coil changes with time.

¨ Lenz’s law tells the positive direction of the induced emf, represented by the minus sign in Faraday’s law.

E = −N ΔΦΔt

= −NΦfinal −Φinitial

tfinal − tinitial

The direction of the induced current is such that the induced magnetic field opposes the change in the flux.

Clicker question: 18

Demo: 29

¨ Wire and magnet¤ Demonstration of induction.

n Number of loopsn How fast the wire is moved.

Φ = BAcosθ

E = −N ΔΦΔt

Example: 210

¨ A wire loop is placed in a magnetic field that is perpendicular to its plane. The field varies with time as shown. Rank the six regions of time in order of increasing magnitude of the induced emf. Indicate ties where appropriate.

Electric guitar pickups11

¨ The permanent magnet magnetizes the metal string.

¨ As the magnetized string vibrates above the coil, the magnetic flux in the coil changes.

¨ Emf is induced in the coil.

Dynamic microphone12

¨ Dynamic microphones employ a stationary permanent magnet and a wire coil attached to a movable diaphragm.

Magnetoencephalography (MEG)13

¨ MEG can measure the small current flowing in the human body using the weak magnetic field it produces.

¨ The change in magnetic field induces emfs in SQUIDs(superconducting quantum interference devices).

¨ In a MEG, the induced emfs are measured at many points just outside the cranium.

Clicker question: 214

Example: 315

¨ The magnetic field shown in the figure decreases uniformly from Bi = 1.0 T to Bf = 0.4 T in Δt = 1.2 s. A loop with a radius r = 3.0 cm and a resistance R = 0.010 Ω is perpendicular to the field. What is the size and direction of the current induced in the loop?

Example: 416

¨ An emf is induced in a conducting loop of wire L = 1.22 m long as its shape is changed from square to circular. Find the average magnitude of induced emf if the change in shape occurs in Δt = 4.25 s and the local magnetic field, B = 0.125 T, is perpendicular to the plane of the loop.

Clicker question: 317