Electromagnetic Induction • Changing magnetic fields can induce electric potential differences.

• Changing flux and the

resulting induced potential difference is responsible for devices ranging from transformers to magnetic brakes.

• This connection of

magnetism and electricity is responsible for some truly remarkable effects.

Remember: The Electromagnetic Flowmeter

qE = qvB E=

∆V d

v= v=

Related to: Motional emf

ΔV = vlB

E B

ΔV Bd

To get a noticeable effect...

ΔV = vlB

Long wire, high speed: 3500 V

To get a noticeable effect...

ΔV = vlB

Flux

A shark is sensitive to a potential difference of 5 nV. If the shark’s head is 0.60 m wide, and it swims at 2.0 m/s in a location where the dip angle is 60°: • What is the potential difference in the earth’s field? • What is the smallest vertical field the shark can sense?

Changing Flux Induces an emf

Current meter Induced! field

N

0

Induced! current

A magnetic field goes through a loop of wire as below. If the magnitude of the magnetic field is decreasing, what will be the direction of the current in the loop? A. Clockwise B. Counterclockwise

x x x x x x x x

x x x x x x x x

x x x x x x x x

x x x x x x x x

xx xx xx xx xx xx xx xx

x x x x x x x x

x x x x x x x x

x x x x x x x x

x x x x x x x x

A loop of wire is connected to a battery and a switch as below. We’ll start counting time at t=0 seconds. The switch is closed at t=1 second and then opened at t=2 seconds. a. Sketch a graph of the current in the upper loop as a function of time, with clockwise current as positive. b. Sketch a graph of the current in the lower loop as a function of time, with clockwise current as positive.

Changing Flux Induces an emf

And if there are N turns in the coil...

A coil of copper wire has 1200 turns, and an area of 0.0040 m2. The coil of wire is connected to a light emitting diode that requires a minimum of 2.0 V to light. A cow magnet with field strength 0.050 T is quickly thrust into the coil. What is the approximate minimum time for the magnet to go from being outside the coil to being inside the coil in order that the resulting emf light the LED?

Which is the most likely pole arrangement for the magnet in the “Dynamo” flashlight shown in class?

Why is the light brighter when the magnet spins at a greater rate?

Changing Flux Induces an emf in Transformers

Changing Flux Requires AC Electricity

the current loop? Section 24.7 Magnetic Fields Exert Torques on Dipoles 45. || The two 10-cm-long parallel wires in Figure P24.45 are sepa40. || People have proposed driving motors with 2the earth’s mag-rated by 5.0||mm. what valuetravels of the resistor will the force 46. AnForelectron withR speed 1.0 * 107 m/s between the We can model the ring a transformer. Thea iron 38. || A current loop inshooter a motor has as an area of 0.85 cm . It carries between the two wires be 5.4 * 10-5 N? netic field. This is possible in principle, but the small field means mAshooter current in a uniform fieldturns of 0.62 T. is theon magnitwo parallel charged plates shown in Figure P24.46. The plates core of the240 ring has 400 ofWhat wire it. When that unrealistically large currents neededloop? to produce noticeable tude of the maximum torque onare the current are separated by 1.0R cm and are charged by a 200 V battery. 2.0 æ the power on, there aeach current A in 39. is ||Suppose Aswitched squareacurrent loop 5.0 cm is on carries a about 500 mA torques. 20-cm-diameter loop ofside wire is of oriented for60 maxiWhat magnetic field strength and direction will allow the eleccurrent. The loopinduces is in a 1.2 Tauniform magnetic field.ring, The axis this primary coil. This current inwould the which 9.0 V 10 cm 9.0 V mum torque in the earth’s field. What current it need to carry tron to pass between the plates without being deflected? of the loop, perpendicular to the plane of the loop, is 30° away -3 looksinlike the secondary of a transformer with a single turn # order from to experience a veryWhat modest * 10 ofN m torque? the field direction. is the1.0 magnitude the torque on 5.0 mm FIGURE P24.45 of41.wire. the current loop? || a. What is the magnitude of the torque on the circular cur40. || People have proposed driving motors with the earth’s mag46. ||inAn electron travels with speed 1.0 * 107 m/s between the rent loop in Figure P24.41? Approximately what the ring netic field. Thiscurrent is possible inwould principle,be but induced the small fieldinmeans v The plates 1.0 cm two parallel charged plates shown in Figure P24.46. b. What is the loop’s stable are equilibrium position? that unrealistically large circumstances currents needed to are produce ideal circumstances? (The farnoticeable from ideal, u

a 20-cm-diameter loop of wire is oriented for maxiand so the torques. actualSuppose current isfield. much less.) mum torque in the earth’s2.0 cmWhat current would it need to carry in order to experience a very modest 1.0 * 10-3 N # m torque?

41. || a. What is the magnitude of the torque 2.0 on the mmcircular curWire rent loop 2.0 Ain Figure P24.41? b. What is the loop’s stable equilibrium 0.20 A position? FIGURE P24.41 2.0 cm

are separated by 1.0 cm and are charged by a 200 V battery. What magnetic field strength FIGURE P24.46and direction will allow the electron to pass between the plates without being deflected?

47. || The two springs in Figure P24.47 each have a spring constant of 10 N/m. They are stretched by 1.0 cm when a current passes v 1.0 cm through the wire. How big is the current? u

FIGURE P24.46

Section 24.8 Magnets and Magnetic Materials

47. || The two springs in Figure P24.47I each have a spring constant of 10 N/m. They are stretched by 1.0 cm when a current passes A All ferromagnetic materials have0.20 a Curie temperature, a tem-through the wire. How big is the current? FIGURE P24.41 2.0 A

Wire

2.0 mm

42. | perature above which they will cease to be magnetic. Explain in Section 24.8 Magnets and Magnetic Materials some detail why you might expect this to be so. 15 cm I 1.2 V | All ferromagnetic materials temperature, a tem-P24.43. 20 cm 43. | A42. solenoid is near a piece of have iron,a Curie as shown in Figure perature above which they will cease to be magnetic. Explain in When asome current is present in the solenoid, a magnetic field is detail why you might expect this to be so. 15 cm 1.2 V 20 cm created. magnetic magnetize iron, and there 43. | This A solenoid is near afield piece will of iron, as shown in the Figure P24.43. current is presentthe in the solenoid,and a magnetic field is B = 0.50 T will be aWhen net aforce between solenoid the iron. B = 0.80 T created. This magnetic field will magnetize the iron, and there a. Make a sketch showing the direction of the magnetic field = 0.50 T will be a net force between the solenoid and the iron. B = 0.80 T FIGUREB P24.47 FIGURE P24.48 froma. the solenoid. On your label the induced Make a sketch showing the sketch, direction of the magnetic field north FIGURE P24.47 FIGURE P24.48 from the solenoid. On your sketch, label the induced north magnetic pole and the induced south magnetic pole in the 48. || A device called a railgun uses the magnetic force on currents called a railgun uses the magnetic force on currents iron. magnetic pole and the induced south magnetic pole in the 48. || A device to launch projectiles at very high speeds. An idealized model of iron. to launch projectiles at very high speeds. An idealized model of b. Willb.the force on the iron or repulsive? a railgunin is illustrated Figure Will the force on the ironbe be attractive attractive or repulsive? a railgun is illustrated Figure P24.48. Ain1.2 V powerP24.48. supply isA 1.2 V power supply is c. Suppose this force moves iron.Which Which will c. Suppose this force movesthe the iron. wayway will the ironthe ironconnected toconnected two conducting rails. A segment of copper in to two conducting rails.wire, A segment of copper wire, in a region of uniform magnetic field, slides freely on field, the rails. The freely on the rails. The move? move? a region of uniform magnetic slides wire has a 0.85 mΩ resistance and a mass of 5.0 g. Ignore the Current in solenoid Piece of iron is hasWhen a 0.85 resistance andon, a mass of 5.0 g. Ignore the mΩ supply resistance ofwire the rails. the power is switched is clockwise as lined up of withiron the is Current in solenoid Piece viewed from the axis of the resistance a. What is the current? of the rails. When the power supply is switched on, is clockwise as lined up with the right end. solenoid. b. What area.theWhat magnitude andcurrent? direction of the force on the viewed from the axis of the is the right end. solenoid. wire? arespeed the after magnitude direction of the force on the c. What willb.beWhat the wire’s it has slid and a distance of wire? 6.0 cm? FIGURE P24.43 49. ||| Irrigationc. channels require regular flow monitoring are it has slid a distance of Whatthat will be the wire’s speed after often equipped with electromagnetic flowmeters in which the 6.0 cm? magnetic field is produced by horizontal coils embedded in the FIGURE P24.43 ||| Irrigation channels require flow monitoring are General Problems bottom49. of the channel. A particular coilthat has 100 turns regular and a diameter of often 6.0 m. When it’s time for aelectromagnetic measurement, a 5.0 A equipped with flowmeters in which the 44. | The right edge of the circuit in Figure P24.44 extends into current is turned on. The large diameter of the coil means that magnetic field is produced by horizontal coils embedded in the a 50 mT uniform magnetic field. What are the magnitude and the field in the water flowing directly above the center of the General Problems bottom equal of the channel. particular coil has 100 turns and a direction of the net force on the circuit? coil is approximately to the field in theAcenter of the coil. a. What is the magnitude the field at the center the coil? diameter ofof6.0 m. When it’s of time for a measurement, a 5.0 A 3.0 æ is directed downward thelarge water is flowing of the coil means that 44. | The right edge of the circuit in Figure P24.44 extends intob. If the field current is turned on.and The diameter east, what is the direction of the force on a positive ion in the 15 V 10 cm What are the magnitude and a 50 mT uniform magnetic field. the the field inofthe water above center the water coil? flowing directly above the center of the direction of the net force on the circuit? coil is approximately equal field c. If the water is flowing above the center of theto coilthe at 1.5 m/s,in the center of the coil. FIGURE P24.44 B = 50 mT what is the magnitude of the force on an ion with a charge a. What is the magnitude of the field+e? at the center of the coil? 3.0 æ b. If the field is directed downward and the water is flowing east, what is the direction of the force on a positive ion in the 15 V 10 cm water above the center of the coil? c. If the water is flowing above the center of the coil at 1.5 m/s, FIGURE P24.44 800 KNIG9721_03_chap_24.indd 03/10/13 PM B = 50 mT what is the magnitude of the force on an ion with1:54 a charge +e?

IG9721_03_chap_24.indd 800

Warming Up...

Positive = clockwise

Warming Up... The figure shows a 10-cm-diameter loop in a magnetic field. The loop’s resistance is 0.1 Ω. For the induced current, determine: a. the direction b. the magnitude xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx

This power pack for a portable stereo delivers 1.0 A at a voltage of 9.0 V under normal operation. It has 400 turns of wire on the primary coil. •What is the power output? •How many turns of wire are on the secondary? •What are the voltage and current in the primary?

Time (s)

Field (T)

0.0

0.50

1.0

0

Eddy currents

Sense of force opposes motion.

Your Brain is a Conductor. Your Skull is Not.

Transcranial magnetic stimulation can aid depression

In a typical pulsed-field TMS machine, the current near the coil will go from 0 T to 2.5 T in a time of 200 µs. A technician holds his hand near the device, with the increasing field directed along the axis of his hand, so the flux goes through his 2.0 cm diameter gold wedding band. What emf is induced in the ring?

Energy Connections

Bringing it All Together

ΔV = vlB

F = IlB

And a Practical Question:

Time and magnetic field exposure may weaken the strength of the magnetization on a credit card strip. Why does swiping the card more rapidly make it more likely to be read?