Download Lesson Plan - GK-12 at Harvard University

JASON BELLORADO
[email protected]
GK-12 PROGRAM - HARVARD UNIVERSITY
PHYSICS FIRST! - HONORS OPTION
MAGNETISM, INDUCTION AND MOTORS
JANUARY 6, 2004
MAGNETISM BASICS:
Two bar magnets exert a force on one another. If 2 north poles (or 2 south poles) are
closely positioned, a repulsive force is produced (see (a) below). If a north pole and a
south pole are brought near, then a force of attraction results (see (b) below).
(a) Repulsive force results between like poles.
(b) Attractive force results between unlike poles.
MAGNETIC FIELD LINES: A magnetic field (which flows from the north to the south pole
of a magnet) surrounds every magnet (see figure below).
Question: What is a magnetic field?
Answer: Magnetic fields exert forces on moving charges (remember, electrical current is
defined as the net movement of positive electrical charges). A magnetic field is a way of
understanding how magnets affect moving charges.


The units of magnetic field are Teslas (T).
It is important to understand how electricity and magnetism are related.
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FORCE ON A CHARGED PARTICLE MOVING IN A MAGNETIC FIELD (RIGHT HAND RULE):
An electrically charged particle (+q) moving through a magnetic field (B) at a velocity
(v) is acted upon by a force (F) (see below).
B (out of page)
The direction of the force can be determined from the Right Hand Rule.
1. Place the fingers of your right hand in the direction of the magnetic field (B).
2. Place the thumb of your right hand in the direction of the motion of the positive
charge.
3. The force applied to the moving charge is in the direction your palm is facing.
Note: The force applied to a moving negative charge is in the opposite direction as the
force applied to a positive moving charge.
Remember, electrical current is defined as the net movement of positive charge.
Therefore, a wire carrying electrical current through a magnetic field will be acted upon
by a force.

The magnitude of the force exerted on a moving positive charge moving through a
magnetic field is given by the following equation:
F  q  v  B  sin  
o
o
o
o
o
(1)
F = induced force (Newtons)
q = magnitude of charge (Coulombs)
B = magnitude of magnetic field (Teslas)
v = velocity of moving charge (meters per second)
 = angle between magentic field direction and direction of charge
propagation
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ELECTROMAGNETIC INDUCTION:
MAGNETIC FLUX: Is a measure of the magnetic field through an area.
Lets consider a loop of wire sitting in a magnetic field:
Wire Loop (area = A)

The magnetic flux is calculated as the product of the magnetic field (B) and the area of
the region being considered that is perpendicular to the magnetic field.
 The units of magnetic flux are Teslas  square meters (Tm2).
For the example shown above, if the loop has area A, the magnetic flux is given as,
B  B  A
(2)
Now consider a loop that is arbitrarily positioned with respect to the magnetic field (see
figure below).
In this case, the magnetic flux is given by,
 B
 B  A  cos  
(3)
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Where  is the angle between the magnetic field lines and the normal (perpendicular) to
the loop.
Note: cos(0°) = 1, cos(60°) = ½, cos(90°) = 0.
The flux can changes when:
1. The magnetic field changes.
2. The area of the loop changes.
3. The angle between the magnetic field and the loop changes.
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FARADAY’S LAW OF INDUCTION:

A voltage (also known as an Electro-Motive Force or emf) is induced in a coil of wire
when the magnetic flux through the coil varies over time.
 The magnitude of the induced emf depends on the change in magnetic flux and the
time required for the change in flux through the area of the loop, and is given by the
following equation:
  N

 B
t
(4)
o  = induced emf (or voltage) (in volts)
o N = number of turns in the coil
o B = change in magnetic flux (in Teslas  square meters)
o t = change in time (in seconds)
The polarity of the induced voltage can be determined using the Right Hand Rule.
Example: Consider a wire loop that consists of 100 turns and has area .25 m2. The loop
initially sits in a magnetic field of 5 Teslas as shown in (a) below. The loop is turned as
shown in (b) below over a period of 3 seconds. What is the induced emf?
a) position of coil at t = 0 seconds
b) position of coil at t = 3 seconds
Solution:
Using equation (3), the magnetic field for a) and b) are calculated as,
a) B = ABcos() = (.25) (5) cos(0) = 1.25 Tm2
b) B = ABcos() = (.25) (5) cos(45) = .8839 Tm2
Using equation (4) the induced emf is,
 = -NB/t = -(100) (1.25-.8839)/3 = -12.2039 volts
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MOTIONAL VOLTAGE (EMF):
Consider the situation in which a conducting rod or wire is moved through a magnetic
field (see figure below).

The conducting rod consists of atoms that are made up of charged particles (protons
(+) and electrons (-)).
 Charged particles moving through a magnetic field are acted upon by a force. The
direction of this force is determined from the Right Hand Rule.
 Since the magnetic field is into the page, and the velocity of the charged particles is to
the right, then,
a) An upwards force is exerted on positively charged particles.
b) A downwards force is exerted on negatively charged particles.
 Thus, a voltage is induced in the moving bar.
What happens when the conducting rod is again moved through a magnetic field, but it is
done so while connected to a circuit? (see figure below)



Because the charged particles can flow around a circuit, a current is produced.
The magnitude of the current that is induced can be calculated using Faraday’s Law
of Induction and Ohm’s Law (V = IR). You will make this calculation on your
worksheet.
Note: Because current is flowing from bottom to top of the moving bar, and because
the bar is in a magnetic field, there will be a force exerted on the bar. Using the Right
Hand Rule, the force will be to the left. The force will ALWAYS act to oppose the
motion of the bar.
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ELECTRIC MOTORS:
The concept behind a motor is to use electricity to start and keep something spinning. An
example is shown below:
contact



contact
Two magnets (north and south) are placed a distance apart such that a magnetic field
(B) exists from north to south.
A circuit is set up so that current flows as shown above through the magnetic field.
(note: the center piece (shown as a thick solid line) is called the rotor and is free to
rotate around. The contacts only touch this piece, but do not hold it.)
Consider the part of the circuit inside of the magnetic field:
o On the left branch, the current is flowing upwards and, thus, a force will be
exerted on the wire.
o Using the Right Hand Rule, the force is determined as going into the page.
o On the right branch, the current is flowing downwards and, using the Right
Hand Rule, it is seen that the force is exerted in the direction coming out of
the page.
o Since the rotor is free to rotate, it will spin in direction shown in the figure.
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