PHYS 1110 Lecture 8 Professor Stephen Thornton September 20, 2012

If there is a current in the loop in the direction shown, the loop will: A) move up B) move down C) rotate clockwise D) rotate counterclockwise E) both rotate and move N S NS B field out of North B field into South Reading Quiz

right out of the page up downward clockwise Look at the north pole: here the magnetic field points to the right and the current points out of the page. The right-hand rule says that the force must point up. At the south pole, the same logic leads to a downward force. Thus the loop rotates clockwise. N S F F A) move up B) move down C) rotate clockwise D) rotate counterclockwise E) both rotate and move If there is a current in the loop in the direction shown, the loop will: Reading Quiz

Discuss when Midterm Exam 1 will be. Then determine homework 2 due date. When would you prefer Exam 1? A)Thursday, September 27 B)Tuesday, October 2 C)Thursday, October 4

Helical Motion in a Magnetic Field

What happens if we form a loop with the current carrying wire? Do demo with wire loop in magnetic field B. (galvanometer demo) We find that the loop rotates in opposite directions depending on the direction of the current!

Magnetic Forces on a Current Loop Forces cause a torque I I I F total = 0

Magnetic Torque on a Current Loop Wire: width w height h F=IhB Area = A = hw Wires affected are into screen

Magnetic Force on Current Loops Consider a rectangular loop in a constant magnetic field. Can also have N loops. Can easily find the force on each side of the loop Forces cancel but, depending on orientation, there may be a torque Loop We define the magnetic dipole moment of the coil to be

Magnetic Torque on a Current Loop We showed the torque to be We can rewrite this in vector form to be where we have used N loops and the magnetic dipole moment,

Potential Energy of Magnetic Dipole We can show (but not going to do) that the potential energy of a magnetic dipole moment in a magnetic field is

Magnetic Torque on a Current Loop The torque rotates loop until vectors are parallel to Loop of wire

Copyright © 2009 Pearson Education, Inc. A galvanometer takes advantage of the torque on a current loop to measure current; the spring constant is calibrated so the scale reads in amperes. Remember that all analog ammeters use a galvanometer. Galvanometer

Copyright © 2009 Pearson Education, Inc. An electric motor uses the torque on a current loop in a magnetic field to turn magnetic energy into kinetic energy. Do electric motor demo

B I A) left B) right C) zero D) into the page E) out of the page Conceptual Quiz A vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?

parallel zero When the current is parallel to the magnetic field lines, the force on the wire is zero. B I A) left B) right C) zero D) into the page E) out of the page Conceptual Quiz A vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire?

Hans Oersted, a Danish physicist, discovered this in 1820 while entertaining students and friends at home. He was preparing a physics lecture.

Now we can imagine combining some of these effects. We know that a current carrying wire produces a magnetic field. We also know that a current carrying wire feels a force in a magnetic field. If we have two wires, can we use one wire to produce a magnetic field at the position of the second wire? Yes! If the second wire carries a current, then it should feel a force! Do demo – next slide.

We have to look closely at fields and forces to see how the forces occur.

We do this experiment to show that current carrying wires exert forces on each other.

Magnetic field due to current moving through a coil of wire.

Note similarity between B of a bar magnet and B of a coil of wire.

The Solenoid B=  0 nI

MRI: Magnetic Resonance Imaging

Copyright © 2009 Pearson Education, Inc. Almost 200 years ago, Michael Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus: Induced EMF

Do demos about induced currents. Push and pull magnet in and out of coils of wire to show current production.

Induced Current Produced by a Moving Magnet

Copyright © 2009 Pearson Education, Inc. Therefore, a changing magnetic field induces an emf/current. Faraday’s experiment used a magnetic field that was changing because the current producing it was changing; the previous graphic shows a magnetic field that is changing because the magnet is moving. Induced EMF

Magnetic Induction B linked by iron bar.

We conclude that it is the change in magnetic flux that causes induced current.

Faraday’s Discovery and the Law of Induction There are many ways to change the magnetic flux through a surface: Move the magnet Turning current on or off in one loop induces current in another Move the loop Change the shape (and the area) of the loop

The Magnetic Flux Through a Loop

Look at the mathematics. This is called Faraday’s Law of Induction after Michael Faraday.

Do some more demos. 1) Magnet through coil again. 2) Flash bulb 3) LED coil

Lenz’s Law The induced current will always be in the direction to oppose the change that produced it.

Applying Lenz’s Law to a Magnet Moving Toward and Away From a Current Loop Induced current

Conceputal Quiz In order to change the magnetic flux through the loop, what would you have to do? A) drop the magnet B) move the magnet upwards C) move the magnet sideways a lot D) Only A and B E) A, B, and C

any direction Moving the magnet in any direction would change the magnetic field through the loop and thus the magnetic flux. Conceptual Quiz In order to change the magnetic flux through the loop, what would you have to do? A) drop the magnet B) move the magnet upwards C) move the magnet sideways a lot D) only A and B E) A, B, and C

If a North pole moves toward the loop from above the page, in what direction is the induced current? A) clockwise B) counterclockwise C) no induced current Conceptual Quiz

If a North pole moves toward the loop from above the page, in what direction is the induced current? A) clockwise B) counterclockwise C) no induced current into the page larger out of the pagecounterclockwise The magnetic field of the moving bar magnet is pointing into the page and getting larger as the magnet moves closer to the loop. Thus the induced magnetic field has to point out of the page. A counterclockwise induced current will give just such an induced magnetic field. Conceptual Quiz Follow-up: What happens if the magnet is stationary but the loop moves?

Motional emf What happens when we push rod down?

Determining the Direction of an Induced Current We exert force to push bar down.

Motional emf

Find force and energy

x x x x x x A wire loop is being pulled through a uniform magnetic field. What is the direction of the induced current? A) clockwise B) counterclockwise C) no induced current Conceputal Quiz

magnetic flux through the loop is not changingno current is induced Since the magnetic field is uniform, the magnetic flux through the loop is not changing. Thus no current is induced. x x x x x x A wire loop is being pulled through a uniform magnetic field. What is the direction of the induced current? A) clockwise B) counterclockwise C) no induced current Conceptual Quiz Follow-up: What happens if the loop moves out of the page?

A conducting rod slides on a conducting track in a constant B field directed into the page. What is the direction of the induced current? x x x x x x x x x x x v A) clockwise B) counterclockwise C) no induced current Conceptual Quiz

A conducting rod slides on a conducting track in a constant B field directed into the page. What is the direction of the induced current? x x x x x x x x x x x v into the page increasing out of the page counterclockwise, The B field points into the page. The flux is increasing since the area is increasing. The induced B field opposes this change and therefore points out of the page. Thus, the induced current runs counterclockwise, according to the right-hand rule. A) clockwise B) counterclockwise C) no induced current Conceptual Quiz Follow-up: What direction is the magnetic force on the rod as it moves?

Copyright © 2009 Pearson Education, Inc. A generator is the opposite of a motor – it transforms mechanical energy into electrical energy. This is an ac generator: The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings. See next slide. Electric Generators

An Electrical Generator Produces AC power Magnetic flux changes! Current is induced

A Simple Electric Motor/Generator

Copyright © 2009 Pearson Education, Inc. If the loop is rotating with constant angular velocity ω, the induced emf is sinusoidal: For a coil of N loops, Induced power:

A generator has a coil of wire rotating in a magnetic field. If the rotation rate increases, how is the maximum output voltage of the generator affected? A) increases B) decreases C) stays the same D) varies sinusoidally Conceptual Quiz

sin(  t)   = NBA   increases   must increase The maximum voltage is the leading term that multiplies sin(  t) and is given by   = NBA . Therefore, if  increases, then   must increase as well. A generator has a coil of wire rotating in a magnetic field. If the rotation rate increases, how is the maximum output voltage of the generator affected? A) increases B) decreases C) stays the same D) varies sinusoidally Conceptual Quiz

Conceptual Quiz: Look at the demonstration of the large electromagnet. Observe what happens (spark) when the switch is opened. What best explains this? A) The battery voltage is leaking through. B) The steady current passing through the magnet. C) Induces a large back current (back emf). D)

Answer: C Nature doesn’t want the magnetic flux to change, so it induces a large current (back emf) to produce a magnetic field. This emf results in the spark across the switch.

Inductance and Inductors Faraday’s Law: Changing current in a circuit will induce emf in that circuit as well as others nearby Self-Inductance: Circuit induces emf in itself (source of back emf) Mutual Inductance: Circuit induces emf in second circuit

Inductance The inductance L is a proportionality constant that depends on the geometry of the circuit

Changing Current in an Inductor Switch open. No current flowing. Switch closed. Inductor opposes magnetic flux change. Induces current to oppose battery current; current rises more slowly. Inductor

Magnetic field energy We know that a battery has to do work to cause current to flow. Similarly an inductor has to do work to cause an induced current to flow from 0 to I in time T. This energy comes from the magnetic field.

There will be a magnetic flux in Loop 1 due to current I 1 flowing in Loop 1 and due to current I 2 flowing in Loop 2. Now it is clearer why we call L self inductance and M mutual inductance.

Copyright © 2009 Pearson Education, Inc. Mutual Inductance A long thin solenoid of length ℓ and cross-sectional area A contains N 1 closely packed turns of wire. Wrapped around it is an insulated coil of N 2 turns. All the flux from coil 1 (the solenoid) passes through coil 2. The magnetic flux between the two coils is linked. We call this mutual inductance.

Copyright © 2009 Pearson Education, Inc. Unit of inductance: the henry, H: 1 H = 1 V·s/A = 1 Ω·s. A transformer is an example of mutual inductance.

Solenoid Self-Induction

Consider an inductor For a solenoid

General energy density

We can produce an emf by using AC voltage and coils. Show demo of AC coils and light bulb

Do transformer demo

Transformer equation

Copyright © 2009 Pearson Education, Inc. This is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary:

Lots of applications for transformers, the bug zapper.

Power distribution Transformers work only if the current is changing; this is one reason why electricity is transmitted as ac.

120 V What is the voltage across the lightbulb? A) 30 V B) 60 V C) 120 V D) 240 V E) 480 V Conceptual Quiz

first transformer2:1 ratio voltage doubles second transformer 1:2 ratiovoltage is halved same as the original voltage The first transformer has a 2:1 ratio of turns, so the voltage doubles. But the second transformer has a 1:2 ratio, so the voltage is halved again. Therefore, the end result is the same as the original voltage. 120 V 240 V 120 V What is the voltage across the lightbulb? A) 30 V B) 60 V C) 120 V D) 240 V E) 480 V Conceptual Quiz

A) greater than 6 V B) 6 V C) less than 6 V D) zero A 6 V battery is connected to one side of a transformer. Compared to the voltage drop across coil A, the voltage across coil B is: AB 6 V Conceptual Quiz

The voltage across B is zero changing dc current The voltage across B is zero. Only a changing magnetic flux induces an emf. Batteries can provide only dc current. A) greater than 6 V B) 6 V C) less than 6 V D) zero AB 6 V Conceptual Quiz A 6 V battery is connected to one side of a transformer. Compared to the voltage drop across coil A, the voltage across coil B is: