Lecture 30 Motional Emf

LECTURE 30 MOTIONAL EMF

Instructor: Kazumi Tolich Lecture 30

¨ Reading chapter 23-3 & 23-4. ¤ Motional emf ¤ Mechanical work and electrical energy Clicker question: 1

3 Motional emf

¨ As the rod moves to the right at a constant velocity v, the motional emf is given by ΔΦ BΔA lvΔt E = N = = B = Bvl Δt Δt Δt Example: 1

¨ A Boeing KC-135A airplane has a wingspan of L = 39.9 m and flies at constant altitude in a northerly direction with a speed of v = 240 m/s. If the vertical component of the Earth’s magnetic -6 field is Bv = 5.0 × 10 T, and its -6 horizontal component is Bh = 1.4 × 10 T, what is the induced emf between the wing tips? Clicker question: 2 & 3

6 Mechanical and electric powers

¨ Suppose the rod is moving with a constant velocity �.

¨ The mechanical power delivered by the external force is:

¨ Compare this to the electrical power in the light bulb:

¨ Therefore, mechanical power has been converted directly into electrical power. Example: 2

¨ In the figure, let the magnetic field strength be B = 0.80 T, the rod speed be v = 10 m/s, the rod length be l = 0.20 m, and the resistance of the resistor be R = 2.0 Ω. (The resistance of the rod and rails are negligible.)

a) Find the induced emf in the circuit.

b) Find the induced current in the circuit (including direction).

c) Find the force needed to move the rod with constant speed (assuming negligible friction).

d) Find the power delivered by the force found in Part c).

e) Find the rate of Joule heating in the resistor. Eddy currents

¨ Consider a sheet of conductor pulled through a magnetic field. There will be induced current called eddy currents although there are now no well-defined current paths.

¨ The magnetic force due to the eddy currents opposes the motion of the conductor to the right (magnetic damping).

¨ Eddy currents can be reduced by increasing the resistance of the possible paths for the eddy currents.

Insulating glue between the metal slabs.

Slots cut into the metal slab. Triple beam balance damping

¨ A metal plate attached to the balance arm passes between the poles of a permanent magnet.

¨ The induced eddy current provides the damping. Clicker question: 4

11 Demo: 1

¨ Magnet down a copper tube

¨ Magnet down an aluminum channel

¨ Magnetic damping pendulum

¨ Flying ring ¤ Demonstrations of eddy current and magnetic force Induction stove

¨ A conducting coil just beneath the cooking surface carries an oscillating current, producing an oscillating magnetic field.

¨ This induces an oscillating eddy current in the conducting cooking pan.

¨ Due to the resistance of the pan, this eddy current heats up the pan.

¨ The cooking surface itself might never get hot. Metal detectors and traffic lights

¨ Metal detectors operate by induced currents.

¨ High frequency alternating current flows in the transmitter coil, which induces eddy current in conductors nearby.

¨ The induced B due to the eddy current opposes the change in the field from the transmitter.

¨ A receiver coil detects the reduction in the magnetic fields from the transmitter and registers the presence of metal.