P132 ch29 PDF
P132 ch29 PDF
P132 ch29 PDF
Magnetism has been known as early as 800BC when people realized that certain stones
could be used to attract bits of iron.
Experiments using magnets have shown the following:
1) EVERY magnet has two poles which we refer to as north and south.
These poles act in a way similar to electric charge, north and south attract, north repels north,
south repels south.
An important difference between electric charges and magnetic poles is that poles are
ALWAYS found in pairs (N,S) while single electric charges (positive or negative) can be
isolated. For example, if you cut a bar magnet in half each piece will have a N and S pole!
2) The forces between magnets are similar to those between electric charges in that the
magnitude of the force varies inversely with the square of the distance between them.
As we shall see, calculating the direction of the magnetic force is more complicated than the
electric field case.
In the 1800s many experiments illustrated that electricity and magnetism were connected.
1) An electric current can exert a force on a magnet.
2) A magnet was shown to exert a force on a current carrying conductor.
3) An electric current can be induced by moving a magnet near it or by changing the current
in a nearby circuit.
In 1865 J. C. Maxwell writes the equations that unify electricity and magnetism.
(only takes 4 equations!)
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F = qE
Since there is no such thing as a single magnetic pole ( monopole) we can not write
an analogous equation for the relationship between the magnetic field and its force.
From experiments using electrically charged particles moving in regions near a magnet we find:
1) The magnitude of the magnetic force is proportional to electric charge of the particle.
A positively charged particle and negatively charged particle experience forces in opposite
directions.
2) The magnitude of the force is proportional to the magnitude of the particles velocity (v).
3) The magnitude of the force is proportional to the magnitude of the magnetic field (B).
4) The magnitude of the force is proportional to sin() where is the angle between the
velocity and magnetic field vectors.
5) The direction of the force is always perpendicular to both B and v.
Items 1)-5) can be summarized in one equation:
You have seen the cross
product before if you
have studied torques.
F = qv B
| F |= qvB sin
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of v B
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v
v
If the charge is positive then the direction of F is into the page.
If the charge is negative then the direction of F is out of the page.
B
v
=1800
B
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v
=00
B
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HRW 29-5
HRW 29-4
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FB
v
One of the more interesting situations is when we have both electric and magnetic forces. Lets
add a uniform electric field to the above figure. Assume we have a positively charged particle.
region with B out of paper
FB
v
F = qv B + qE
This leads to a procedure that allows us to measure mass to charge ratio of a particle!
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F = qE a x =
qE
m
a x t 2 qEt 2
x = x0 + v x t +
=
2
2m
We can eliminate the time using: t=L/v. Therefore the deflection is:
x=
qEL2
2mv 2
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F = IL B
If the wire is not straight or if the B-field is not uniform we can calculate the force from:
dF = IdL B F = I dL B
Example: How large a magnetic field do we need to suspend a copper wire (mass m, length L) with current I
running through it?
In order to suspend the wire we must counter act gravity, so we require: mg=IBL or B=(mg)/(IL).
For copper m/L is a constant (its mass density)=46.6x10-3kg/m, and using g=9.8 m/s2 we have:
B=0.46/I (Tesla)
If a wire carries 100A then B~5x10-3 T. (This is about 50X the earths magnetic field)
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F = qvB = m
r=
qB
The time it takes for one complete revolution is the circumference of the circle divided by the
particles speed.
distance 2r
1 mv 2m
T=
speed
= 2
v qB
= 2f =
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2 qB
=
T
m
qB
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