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Physics 2. Chapter 20 Section 1. Demonstration Notes. As magnet approaches the coil the B field in the coil increases and a I is produced As magnet leaves the coil the B field in the coil decreases and a I is produced in the opposite direction

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Physics 2

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## Physics 2

Chapter 20

Section 1

### Demonstration Notes

• As magnet approaches the coil the B field in the coil increases and a I is produced

• As magnet leaves the coil the B field in the coil decreases and a I is produced in the opposite direction

• Similar results are achieved when the coil moves instead

### Induction

• Induced current - current brought about by a changing magnetic field

To get a current you need an emf

• Induced emf – emf brought about by a changing magnetic field

### Ways to Induce an emf and a Current

• Change the strength of the magnetic field through the coil

- as magnet moves closer the B field increases

- as magnet moves away the B field decreases

### Ways to Induce an emf and a Current

• Change the area of the coil in a uniform B field

- decreasing area decreases B field passing through

- increasing area increases B field passing through

### Ways to Induce an emf and a Current

• Rotate the coil in a uniform B field

- as the coil rotates the amount of B field perpendicular to the coil’s area changes

Remember: even if your coil is not part of a complete circuit, an emf will still be induced

to have a current the coil has to be part of a complete circuit

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v

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Every q in rod as v to the right so feels F up the rod

+q collects at the top and forms an emf (or potential difference)

q will stop moving when F between + and – charges balances F due to B field

### Motional emf

emf in rod brought about due to motion of charges in a B field

- exists as long as rod moves

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v

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### Motional emf

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Consider a rod sliding on conducting rails

q moves counter-clockwise around loop as long as rod moves

Ε = vBl

where v – speed

B – mag field

l – length of rod

### Motional emf

A

V

Producing an induced emf with the aid of a magnetic field

1 problem with our arrangement!

I in rod is perpendicular to B field so experiences a force opposing the rod’s velocity

To keep rod moving an external force will need to be applied

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### Sample Problem

Suppose a rod is moving at a speed of 5 m/s in a direction perpendicular to a 0.8 T B field. The rod has a length of 1.6 m and has negligible electrical resistance. What is the emf of the rod? Assuming a light bulb having a resistance of 96 ohms is connected, find the induced current in the circuit. What force opposes the motion of the rod?

### Magnetic Flux

Ф = BA cosΘ[Ф] = Tm2 = Weber, Wb

Where Ф – magnetic flux

B – magnitude of magnetic field at

surface

A – area of the surface

Θ – angle between B and the normal

to the surface

### Sample Problem

A rectangular coil of wire is situated in a constant B field whose magnitude is 0.5 T. The coil has an area of 2 m2. Determine the magnetic flux for the orientations of 0, 60, and 90 degrees.

### Magnetic Flux

• Magnetic flux is proportional to the number of B field lines that pass through a surface

• In part c of our example no lines passes through the loop so there was no flux

### Review

• Electromagnetic induction – an emf is brought about by the use of a B field

• Induced emf – voltage brought about by changes in a B field

• Motional emf – voltage brought about by motion through a B field

An induced or motional emf can produce an induced current if connected to a closed pathway.

Assume that R = 6 ohms, l = 1.2 m, and that a uniform 2.5 T magnetic field is directed into the page. At what speed should the bar be moved to produce a current of 0.5 A in the resistor?

F

### Sample Problem

Assume the resistor has a value of 6 ohms. A 2.5 T magnetic field is directed into the paper. Let l = 1.2 m and neglect the mass of the bar. Calculate the force required to move the bar to the right at a constant speed of 2 m/s.

F

### Sample Problem

A 5 sided object whose width is 0.4 m, length is 1.2 m, height is 0.3 m, and slanted face is 0.5 m, is placed in a uniform B field. The B field has a magnitude of 0.25 T and points along the +y direction. Determine the magnetic flux for each of the 5 sides.

y

B

x

### Faraday’s Law of Electromagnetic Induction

• The avg emf induced in a coil of N loops during a time Δt is N times the Δφ through each loop divided by the time

Ε = -N (Δφ / Δt)

Since φ = BAcosΘ we get E if B, A or Θ

change in any way

### Sample Problem

A coil of wire consists of 20 turns, each of which has an area of 0.015 m2. A constant B field is perpendicular to each loop. At time t = 0, the magnitude of the B field at the location of the coil is 0.05 T. At a time of t = 0.1 s, the B field at the coil is now 0.06 T. Find the average emf induced in the coil during this time. What would be the value of the induced emf if the magnitude of the B field decreased from 0.06 T to 0.05 T in 0.1 s?

### Sample Problem

A flat coil of wire has an area of 0.02 m2 and consists of 50 turns. At t = 0 the coil is oriented so its surface is perpendicular to a constant B field of magnitude 0.18 T. The coil is then rotated through an angle of 30 degrees in a time of 0.1 s. Determine the average emf induced. What would be the induced emf if the coil were returned to its initial orientation in the same time of 0.1 s?

### Lenz’s Law

• Polarity of an induced emf is such that the emf would produce a current whose own B field opposes the change in flux that causes the induced emf

induced B field opposes the change in flux, not the flux itself

### Lenz’s Law

To use Lenz’s Law:

• Determine whether the flux is increasing or decreasing

• Find what direction of induced B will oppose the change in flux

• Use RHR to determine the direction of induced current

R

The figure shows a permanent magnet approaching a loop of wire. 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.

### Sample Problem

S N

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There is a constant B field in a rectangular region of space. The field is directed perpendicular to the plane of the paper. Outside this region there is no B field. A copper ring slides through this region, from position 1 to position 5. For each of the 5 positions, determine if an induced I exists in the ring and, if so, the direction of the induced I.

1

2

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5