Embed Size (px)
Citation preview
3EM Induction.notebook
1
May 08, 2014
Induced EMF and Induced Current
3EM Induction.notebook
2
May 08, 2014
Notice: There is NO BATTERY in the secondary circuit!
It is the changing field that produces the current.
ΔB I
3EM Induction.notebook
3
May 08, 2014
The current in the coil is called the induced current because it is brought about by a changing magnetic field.
Since a source emf is always needed to produce a current, the coil behaves as if it were a source of emf. This emf is known as the induced emf.
3EM Induction.notebook
4
May 08, 2014
An emf can be induced by changing the area of a coil in a constant magnetic field.
ΔA I
In each example, both an emf and a current are induced because the coil is part of a complete circuit. If the circuit were open, there would be no induced current, but there would be an induced emf.
The phenomena of producing an induced emf with the aid of a magnetic field is called electromagnetic induction.
3EM Induction.notebook
5
May 08, 2014
Motional Emf
THE EMF INDUCED IN A MOVING CONDUCTOR
Notice that as this rod moves, charges separate, and an emf is induced in the rod.
FB = q v x B
The separated charges on theends of the conductor give riseto an induced emf, called amotional emf.
If you stop moving, you stop the emf.
From where is this energy coming?answer: the hand (which is like the battery in a "normal" circuit
3EM Induction.notebook
6
May 08, 2014
Motional Emf
Motional emf when v, B, and L are mutually perpendicular
calculating motional emf :
E = v B L(really: E = v x B L)
(on formula sheet)
3EM Induction.notebook
7
May 08, 2014
Motional Emf2. Near San Francisco, where the vertically downward component of the earth's magnetic field is 4.8 x 105 T , an emf of 2.4 x 103 V is induced between the sides of the car. (a) Which side of the car is positive (driver's or passengers)?(b) What is the width of the car?
3EM Induction.notebook
8
May 08, 2014
Motional Emf5. The drawing shows three identical rods (A, B, and C) moving in different planes. A constant magnetic field of magnitude 0.45 T is directed along the +y axis. The length of each rod is L = 1.3 m, and the rods each have the same speed, va = vb= vc = 2.7 m/s. For each rod, find the magnitude of the motional emf, and indicate which end (1 or 2) of the rod is positive.
3EM Induction.notebook
9
May 08, 2014
Motional Emf
B = 0.50 T
L = 1.3 m
v = 4.0 m/s
R = 0.75 Ω
3EM Induction.notebook
10
May 08, 2014
MOTIONAL EMF AND ELECTRICAL ENERGY
Motional Emf
In order to keep the rod moving at constant velocity, the force the hand exerts on the rod must balance the magnetic force onthe current:
Fhand = FB = ILB
Lighting this bulb isn't free!
3EM Induction.notebook
11
May 08, 2014
E
Do you know a name for this quantity?
Hint: This quantity has to do with the amount of field lines going through an area.
answer: Magnetic Flux!!!
3EM Induction.notebook
12
May 08, 2014
E = ΔΦBΔt
*(on formula sheet)
* Usually you'll see this written with a "" sign before it. That negative sign says that the direction of the current induced in the circuit is such that the magnetic force acts on the rod to oppose its motion and slow it down.
E = ΔΦBΔtBetter way to write this:
E
Don't let the elegance of this fool you; this is the most sublime and profound things human beings have ever discovered!
3EM Induction.notebook
13
May 08, 2014
Electric Flux (flow)Measure of how much of the electric field penetrates (flows through) a given surface.
Remember this: Electric flux is proportional to the number of
electric field lines going through a surface or area.
Smaller Flux Bigger Flux
The flux is proportional to the strength of the field.
3EM Induction.notebook
14
May 08, 2014
The flux is proportional to the area of the surface.
Smaller Flux Bigger Flux
3EM Induction.notebook
15
May 08, 2014
A
EΘ
The flux is also proportional to how the area is oriented.
Area is quantified as vector that points perpendicular to the surface, and is as large as the surface area of the surface.
For which angle of Θ do you get the most flux through a given surface area?
Would this be a cross product or a dot product idea?
3EM Induction.notebook
16
May 08, 2014
Calculating Electric Flux
ΦE = E A = E A cos Θ
3EM Induction.notebook
17
May 08, 2014
Magnetic flux is proportional to both the strengthof the magnetic field passing through the plane ofa loop of wire and the area of the loop.
Magnetic FluxMagnetic flux is defined the same way as electric flux.
A
A
3EM Induction.notebook
18
May 08, 2014
Wilhelm Eduard Weber18041891German
Calculating Magnetic Flux
ΦB = B A = B A cos Θ (on formula sheet, but they use φm)
Units: T m2 = Weber (Wb)
3EM Induction.notebook
19
May 08, 2014
17. A fivesided object, whose dimensions are shown in the drawing, is placed in a uniform magnetic field. The magnetic field has a magnitude of 0.25 T and points along the positive y direction. Determine the magnetic flux through each of the five sides.
3EM Induction.notebook
20
May 08, 2014
Faraday’s Law of Electromagnetic Induction
Joseph Henry17911878American
Michael Faraday17911867British
The usefulness of this idea is obvious!
3EM Induction.notebook
21
May 08, 2014
Faraday’s Law of Electromagnetic Induction
If a circuit contains N tightly wound loops and the flux changes by ΔΦB during a time interval Δt, the average emf induced is given by Faraday’s Law:
E = N ΔΦBt
Don't miss the Δ!
Again, more profound than 99.9% of the ideas you've ever heard!
3EM Induction.notebook
22
May 08, 2014
Faraday’s Law of Electromagnetic Induction
More on the Negative:
E = N ΔΦBt
Heinrich Friedrich Emil Lenz18041865 Russian
Lenz's LawThe current caused by the induced emf travels in the direction that creates a magnetic field with flux opposing the change in the original
flux through the circuit.
3EM Induction.notebook
23
May 08, 2014
The current in the wire is steadily increasing as time goes by. This induces a current in the rectangular loop. What direction does current flow in the rectangular loop?
Example:
3EM Induction.notebook
24
May 08, 2014
The north pole of the magnet moves toward the coil. What direction must the current flow in the coil?
Example:
3EM Induction.notebook
25
May 08, 2014
Example:
A coil of wire is placed near a solenoid. a) When the switch is closed, which way does current flow in the coil? b)What happens when the switch is reopened?
3EM Induction.notebook
26
May 08, 2014
Caution:Some people mistakenly think that Lenz's Law says that the
induced magnetic field is always counter to the external magnetic field.
The graph shows how magnetic field around a loop coil varies with time. Example:
Which way will the induced current flow in the coil?
3EM Induction.notebook
27
May 08, 2014
3EM Induction.notebook
28
May 08, 2014
3EM Induction.notebook
29
May 08, 2014
21. A circular coil (950 turns, radius 0.060 m) is rotating in a uniform magnetic field. At t = 0 , the normal to the coil is perpendicular to the magnetic field. At t = 0.010 s, the normal makes an angle of Φ = 45° with the field because the coil has made oneeighth of a revolution. An average emf of magnitude 0.065 V is induced in the coil. Find the magnitude of the magnetic field at the location of the coil.
3EM Induction.notebook
30
May 08, 2014
