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LECTURE 29 MOTIONAL EMF Instructor: Kazumi Tolich Lecture 29 2 ! Reading chapter 23-4 to 23-5. ! Motional emf ! Mechanical work and electrical energy Motional emf 3 This conducting rod completes the circuit. ! As it falls, the magnetic flux decreases, and a current is induced. ! The motion of the rod produces a motional emf in the system. ! Direction of the induced current 4 To oppose the decrease in magnetic flux through the loop, the induced current must flow in a direction that strengthens the magnetic field within the loop. ! The force due to the induced current is upward, slowing the fall. ! Eddy currents 5 ! ! ! Currents can also flow in bulk conductors. 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. Eddy currents: 2 6 ! 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. Clicker question: 1 7 Demo: 1 8 Magnet down a copper tube ! Magnet down an aluminum channel ! ! Demonstration of eddy current and magnetic force Demo: 2 9 ! Magnetic damping pendulum ! Demonstration of eddy current and magnetic force Triple beam balance damping 10 A metal plate attached to the balance arm passes between the poles of a permanent magnet. ! The induced eddy current provides the damping. ! Demo: 3 11 ! Flying ring ! Demonstration of eddy current and magnetic force Induction stove 12 ! ! ! ! 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 13 ! ! 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. Motional emf: quantitative 14 ! ! An upward magnetic force qvB is on the positive charge carrier moving horizontally with the rod. The charge carriers continue to move upward until the electric force due to the E field by the separated charge is balanced by the magnetic force. FE = FB qE = qvB E = vB E = El = vBl Example: 1 15 ! 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 field is Bv = 5.0 × 10-6 T, and its horizontal component is Bh = 1.4 × 10-6 T, what is the induced emf between the wing tips? Motional emf: quantitative 2 16 ! As the rod moves to the right at a constant velocity v, the motional emf is given by E =N ! ΔΦ BΔA lvΔt = =B = Bvl Δt Δt Δt The electric field caused by the motion of the rod is E = El = Bvl E = Bv ! The induced current is E Bvl I= = R R Forces on the rod 17 If the rod is to move at a constant speed, an external force must be exerted on it. ! This force should have equal magnitude and opposite direction to the magnetic force: ! Mechanical and electric powers 18 ! 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. Clicker question: 2 & 3 19 Example: 2 20 ! 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.