General Physics (PHY 2140) Lecture 16 Electricity and Magnetism Induced voltages and induction Magnetic flux and induced emf Faraday’s law http://www.physics.wayne.edu/~apetrov/PHY2140/ Chapter 20 11/13/2018

Lightning Review Last lecture: Magnetism Ampere’s law and applications Induced voltages and induction Magnetic flux Review Problem: A sphere of radius R is placed near a long, straight wire that carries a steady current I. The magnetic field generated by the current is B. The total magnetic flux passing through the sphere is 1. moI. 2. moI /(4 pR2). 3. 4 pR2 moI 4. zero. 5. need more information 11/13/2018

Recall: right hand rule II 11/13/2018

20.1 Induced EMF and magnetic flux Faraday’s experiment Two circuits are not connected: no current? However, closing the switch we see that the compass’ needle moves and then goes back to its previous position Nothing happens when the current in the primary coil is steady But same thing happens when the switch is opened, except for the needle going in the opposite direction… Picture © Molecular Expressions 11/13/2018 What is going on?

20.2 Faraday’s law of induction Induced current I N S v 11/13/2018

20.2 Faraday’s law of induction v B I N S I A current is set up in the circuit as long as there is relative motion between the magnet and the loop. 11/13/2018

Does there have to be motion? AC Delco - + 1 volt I I (induced) 11/13/2018

Does there have to be motion? AC Delco - + 1 volt 11/13/2018

Does there have to be motion? AC Delco - + 1 volt I (induced) 11/13/2018

Does there have to be motion? NO!! Does there have to be motion? AC Delco - + 1 volt 11/13/2018

Maybe the B-field needs to change….. v B 11/13/2018

Maybe the B-field needs to change….. v B 11/13/2018

Maybe the B-field needs to change….. v B I 11/13/2018

Faraday’s law of magnetic induction In all of those experiment induced EMF is caused by a change in the number of field lines through a loop. In other words, The instantaneous EMF induced in a circuit equals the rate of change of magnetic flux through the circuit. Lenz’s Law: The polarity of the induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop. That is, the induced current tends to maintain the original flux through the circuit. Lenz’s law The number of loops matters 11/13/2018

Applications: Ground fault interrupter Electric guitar SIDS monitor Metal detector … 11/13/2018

Example 1: EMF in a loop A wire loop of radius 0.30m lies so that an external magnetic field of strength +0.30T is perpendicular to the loop. The field changes to -0.20T in 1.5s. (The plus and minus signs here refer to opposite directions through the loop.) Find the magnitude of the average induced emf in the loop during this time. 11/13/2018

and after the field changes the flux is A wire loop of radius 0.30m lies so that an external magnetic field of strength +0.30T is perpendicular to the loop. The field changes to -0.20T in 1.5s. (The plus and minus signs here refer to opposite directions through the loop.) Find the magnitude of the average induced emf in the loop during this time. Given: r = 0.30 m Bi = 0.30 T Bf = -0.20 T Dt = 1.5 s Find: EMF=? The loop is always perpendicular to the field, so the normal to the loop is parallel to the field, so cosq = 1. The flux is then Initially the flux is and after the field changes the flux is The magnitude of the average induced emf is: 11/13/2018

Example 2: EMF of a flexible loop The flexible loop in figure below has a radius of 12cm and is in a magnetic field of strength 0.15T. The loop is grasped at points A and B and stretched until it closes. If it takes 0.20s to close the loop, find the magnitude of the average induced emf in it during this time. A X X X X B 11/13/2018

20.3 Motional EMF l v B F Let's consider a conducting bar moving perpendicular to a uniform magnetic field with constant velocity v. This force will act on free charges in the conductor. It will tend to move negative charge to one end, and leave the other end of the bar with a net positive charge. 11/13/2018

Motional EMF The separated charges will create an electric field which will tend to pull the charges back together. When equilibrium exists, the magnetic force, F=qvB, will balance the electric force, F=qE, such that a free charge in the bar will feel no net force. Thus, at equilibrium, E = vB. The potential difference across the ends of the bar is given by DV=El or A potential difference is maintained across the conductor as long as there is motion through the field. If the motion is reversed, the polarity of the potential difference is also reversed. 11/13/2018

Motional EMF – conducting rails v Dx B We can apply Faraday's law to the complete loop. The change of flux through the loop is proportional to the change of area from the motion of the bar: or (Faraday’s law) 11/13/2018 current Motional EMF

Example: wire in the magnetic field Over a region where the vertical component of the Earth's magnetic field is 40.0µT directed downward, a 5.00 m length of wire is held in an east-west direction and moved horizontally to the north with a speed of 10.0 m/s. Calculate the potential difference between the ends of the wire, and determine which end is positive. 11/13/2018

20.4 Lenz’s law revisited Application of Lenz's law will tell us the direction of induced currents, the direction of applied or produced forces, and the polarity of induced emf's. Lenz's law says that the induced current will produce magnetic flux opposing this change. To oppose an increase into the page, it generates magnetic field which points out of the page, at least in the interior of the loop. Such a magnetic field is produced by a counterclockwise current (use the right hand rule to verify). 11/13/2018

Lenz’s law: energy conservation We arrive at the same conclusion from energy conservation point of view The preceding analysis found that the current is moving ccw. Suppose that this is not so. If the current I is cw, the direction of the magnetic force, BlI, on the sliding bar would be right. This would accelerate the bar to the right, increasing the area of the loop even more. This would produce even greater force and so on. In effect, this would generate energy out of nothing violating the law of conservation of energy. Our original assertion that the current is cw is not right, so the current is ccw! 11/13/2018

S S S N S N N v v The induced flux seeks to counteract the change. 11/13/2018

Example: direction of the current Find the direction of the current induced in the resistor at the instant the switch is closed. 11/13/2018

Applications of Magnetic Induction Tape / Hard Drive / ZIP Readout Tiny coil responds to change in flux as the magnetic domains (encoding 0’s or 1’s) go by. Question: How can your VCR display an image while paused? Credit Card Reader Must swipe card  generates changing flux Faster swipe  bigger signal 11/13/2018