General Physics (PHY 2140) Lecture 18 Electricity and Magnetism Induced voltages and induction Generators and motors Self-induction http://www.physics.wayne.edu/~apetrov/PHY2140/ Chapter 20 9/18/2018

Lightning Review Last lecture: Induced voltages and induction Induced EMF Faraday’s law Motional EMF Review Problem: Two very long, fixed wires cross each other perpendicularly. They do not touch but are close to each other, as shown. Equal currents flow in the wires, in the directions shown. Indicate the locus of points where the net magnetic field is zero. 9/18/2018

Next week: Prof. Claude Pruneau Lectures on Monday and Wednesday Exam on Friday 9/18/2018

20.5 Generators Generators and motors are two of the most important applications of induced emf (magnetic inductance). A generator is something that converts mechanical energy to electrical energy. Alternating Current (AC) generator Direct Current (DC) generator A motor does the opposite, it converts electrical energy to mechanical energy. 9/18/2018

AC Generators Basic operation of the generator As the loop rotates, the magnetic flux through it changes with time This induces an emf and a current in the external circuit The ends of the loop are connected to slip rings that rotate with the loop Connections to the external circuit are made by stationary brushed in contact with the slip rings 9/18/2018

AC generator Compute EMF It is only generated in BC and DA wires EMF generated in BC and DA would be Thus, total EMF is If the loop is rotating with w A B v sin q v B A as v=rw=aw/2 9/18/2018

AC generator (cont) Generalize the result to N loops where we also noticed that A=la Note: is reached when wt=90˚ or 270˚ (loop parallel to the magnetic field) EMF generated by the AC generator 9/18/2018

DC generator By a clever change to the rings and brushes of the ac generator, we can create a dc generator, that is, a generator where the polarity of the emf is always positive. The basic idea is to use a single split ring instead of two complete rings. The split ring is arranged so that, just as the emf is about to change sign from positive to negative, the brushes cross the gap, and the polarity of the contacts is switched. The polarity of the contacts changes in phase with the polarity of the emf -- the two changes essentially cancel each other out, and the emf remains always positive. The emf still varies sinusoidally during each half cycle, but every half cycle is a positive emf. 9/18/2018

Motors A motor is basically a generator running in reverse. A current is passed through the coil, producing a torque and causing the coil to rotate in the magnetic field. Once turning, the coil of the motor generates a back emf, just as does the coil of a generator. The back emf cancels some of the applied emf, and limits the current through the coil. 9/18/2018

Motors and Back emf The phrase back emf is used for an emf that tends to reduce the applied current When a motor is turned on, there is no back emf initially The current is very large because it is limited only by the resistance of the coil 9/18/2018

Example: coil in magnetic field A coil of area 0.10 m² is rotating at 60 rev/s with its axis of rotation perpendicular to a 0.20T magnetic field. (a) If there are 1000 turns on the coil, what is the maximum voltage induced in the coil? (b) When the maximum induced voltage occurs, what is the orientation of the coil with respect to the magnetic field? 9/18/2018

20.6 Eddy currents (application) Magnetic Levitation (Maglev) Trains Induced surface (“eddy”) currents produce field in opposite direction  Repels magnet  Levitates train Maglev trains today can travel up to 310 mph  Twice the speed of Amtrak’s fastest conventional train! May eventually use superconducting loops to produce B-field  No power dissipation in resistance of wires! N S rails “eddy” current 9/18/2018

20.7 Self-inductance When a current flows through a loop, the magnetic field created by that current has a magnetic flux through the area of the loop. If the current changes, the magnetic field changes, and so the flux changes giving rise to an induced emf. This phenomenon is called self-induction because it si the loop's own current, and not an external one, that gives rise to the induced emf. Faraday’s law states 9/18/2018

where L is called the inductance of the device Units: SI: henry (H) The magnetic flux is proportional to the magnetic field, which is proportional to the current in the circuit Thus, the self-induced EMF must be proportional to the time rate of change of the current where L is called the inductance of the device Units: SI: henry (H) If flux is initially zero, 9/18/2018

Example: solenoid A solenoid of radius 2.5cm has 400 turns and a length of 20 cm. Find (a) its inductance and (b) the rate at which current must change through it to produce an emf of 75mV. 9/18/2018

20.9 Energy stored in a magnetic field The battery in any circuit that contains a coil has to do work to produce a current Similar to the capacitor, any coil (or inductor) would store potential energy Summary of the properties of circuit elements. Resistor Capacitor Inductor units ohm, W = V / A farad, F = C / V henry, H = V s / A symbol R C L relation V = I R Q = C V emf = -L (DI / Dt) power dissipated P = I V = I² R = V² / R energy stored PEC = C V² / 2 PEL = L I² / 2 9/18/2018

Example: stored energy A 24V battery is connected in series with a resistor and an inductor, where R = 8.0W and L = 4.0H. Find the energy stored in the inductor (a) when the current reaches its maximum value and (b) one time constant after the switch is closed. 9/18/2018