1. MSTC AP Physics 2
Chapter 20
Section 1

2. Recall Electricity and magnetism are related in two ways:
An electric current produces a magnetic field
A magnetic field exerts a forces on an electric current or a moving electric charge.
Could a magnetic field produce a current?
Ten years later Joseph Henry and Michael Faraday independently made the discovery.
Henry made the discovery first but Faraday published first and investigated the subject in much more detail.
The idea of electromagnetic induction is the basis for many practical devices from generators to alternators to transformers, cds and dvds and computer memory

3. emf
emf (electromotive force) – voltage or electric potential difference that is capable of creating an electric current
- ex – 9 V battery provides 9 V that is capable of
creating a current if connected to a complete
circuit

4. Faraday’s experiment
Faraday set up the arrangement above that consisted of a battery connected to an iron ring. A second wire was connected from the iron ring to an ammeter. Faraday hoped that if he provided a large enough voltage from the battery that current would be produced in the second wire and be detected by the ammeter. The fact that the wires were wound around the iron is important. Iron is a ferromagnetic material. We know the coil of wire on the left will produced a magnetic field. The iron will become magnetized so there will be a magnetic field that passes through the coil on the right.
No luck!
However, Faraday noticed that for a brief moment when he closed the switch, the ammeter registered a current. Likewise, when he opened the switch the ammeter registered a current but in the opposite direction!

5. Induced current
Faraday concluded that although a constant magnetic field produces no current, a changing magnetic field can produce a current.
Induced current – current produced by a changing magnetic field

6. Induced emf
To have a current, there has to be an emf so Faraday concluded that changing the magnetic field was a source of an emf
Induced emf – an emf generated by a changing magnetic field
Note: even if an emf is induced a current might not be produced
- to have an induced current there has to be a complete
circuit

7. Electromagnetic induction
Electromagnetic induction – process of producing an emf and possibly a current by changing a magnetic field
With a magnet and a complete loop of wire we can produce a current
- push magnet into coil get current
- pull magnet out of coil get reversed current
- magnet is stationary you get no current
- if coil has more coils you get a stronger current
- can also move the coil and keep the magnet
stationary to get similar results
Demonstrator with coils of wire and magnets

8. Magnetic flux
Magnetic flux – a measurement that indicates the amount of magnetic field that passes through an area
ΦB = BAcosΘ [ΦB] = T m2 = Weber, Wb
ΦB – magnetic flux
B – strength of the magnetic field
A – area of loop
Θ – angle between B and the normal to the plane of
the loop
Faraday discovered that the strength of the emf and current induced depended on how quickly the magnetic field changes
- It also depends on the number of loops, area of the loops, and the orientation of the loop relative to the magnetic field

9. Magnetic Flux ΦB = BAcosΘ Flux changes if magnetic field changes
Flux changes if the area of the loop changes
Flux changes if the orientation of the loop changes
Maximum flux if the magnetic field passes through the loop (B and normal of A are parallel)
No flux if the magnetic field does not pass through the loop (B and normal of A are perpendicular)

10. Sample Problem
A square loop of wire 10 cm on a side is in a 1.25 T magnetic field. What are the maximum and minimum values of flux that can pass through the loop? What is the flux if the loop makes an angle of 55 degrees with the magnetic field?

11. Sample Problem
A house has a floor area of 112 m2 and an outside wall that has an area of 28 m2. The earth’s magnetic field here has a horizontal component of 2.6 x 10-5 T that points due north and a vertical component of 4.2 x 10-5 T that points straight down toward the earth. Determine the magnetic flux through the wall if the wall faces (a) north and (b) east. (c) Calculate the magnetic flux that passes through the floor.

12. Faraday’s Law of Induction
Faraday’s Law of Induction- the induced emf in a coil depends on the time rate of change of the magnetic flux through all the loops
Є = -NΔΦB / Δt
Є – induced emf
N – number of loops
ΔΦB – change in magnetic flux
Δt – time interval
Negative sign indicates the direction of the induced emf which we will come back to discuss in a minute

13. Faraday’s Law of Induction
Є = -NΔΦB / Δt
An emf is induced whenever a change in flux occurs through the coil
- magnetic field increases or decreases
- size of the loop increases or decreases
- orientation of the loop changes
B field gets stronger the flux increases
B field gets weaker the flux decreases
The loop gets bigger the flux increases
The loop gets smaller the flux decreases
The loop turns from having its area perpendicular to the B field to parallel to the B field the flux goes from a max to zero

14. Sample Problem
A circular loop of wire is placed in a uniform magnetic field that is parallel to the normal to the loop. The strength of the magnetic field is 3 T. The area of the loop begins shrinking at a constant rate of 0.4 m2/s. What is the magnitude of the emf induced in the loop while the area is shrinking?

15. Sample Problem
A circular coil (950 turns, radius = 6 cm) is rotating in a uniform magnetic field. At t = 0 the normal to the coil is perpendicular to the magnetic field and at t = 0.01 s the normal makes an angle of 45 degrees with the field. An average emf of magnitude 65 mV is induced in the coil. Find the magnitude of the magnetic field at the location of the coil.

16. Sample Problem
A 75 turn conducting coil has an area of 85 x 10-3 m2 and the normal to the coil is parallel to a magnetic field B. The coil has a resistance of 14 Ω. At what rate (in T/s) must the magnitude of B change for an induced current of 7 mA to exist in the coil?

17. Lenz’s Law
Lenz’s Law – a current produced by an induced emf moves in a direction so that its magnetic field opposes the original change in flux
The induced magnetic field points in such a direction so as to oppose the change in the flux that causes the induced emf in the first place

18. Lenz’s Law To use Lenz’s Law:
1. Determine whether the magnetic flux is
increasing or decreasing
2. Find the direction of the induced magnetic
field that will oppose the change in the flux
3. Use the right hand rule to determine the
direction of the induced current.

19. Sample Problem
A permanent magnet approaches a loop of wire as shown. The external circuit attached to the loop consists of the resistance R. Find the direction of the induced current and the polarity of the induced emf through the resistor.

20. Sample Problem
In the figure provided there is a constant magnetic field in a rectangular region of space. This field is directed perpendicularly into the plane of the paper. Outside this region there is no magnetic field. A copper ring slides through the region, from position 1 to position 5. For each of the five positions, determine if an induced current exists in the ring and, if so, find the direction of the current.

21. Sample Problem
A square coil of wire with side 5 cm contains 100 loops and is positioned perpendicular to a uniform 0.6 T magnetic field. It is quickly pulled from the field at constant speed (moving perpendicular to B) to a region where B drops abruptly to zero. At t=0, the right edge of the coil is at the edge of the field. It takes 0.1 s for the whole coil to reach the field free region. The coil’s total resistance is 100 Ω. Find (a) the rate of change in flux through the coil, and (b) the emf and current induced.