Download Lecture 17 - McMaster Physics and Astronomy

Magnetism (3 weeks)
CHAPTER 29: Magnetic fields exert a force on
moving charges.
CHAPTER 30: Moving charges (currents) create
magnetic fields.
CHAPTERS 31, 32: Changing magnetic fields create
electric fields. (Induction)
Magnetic fields
•Magnetic poles, forces, and fields
•Force on a moving charged particle
•Force on a current-carrying wire
Magnets and Magnetic Forces
Similar model to electrostatics:
Each magnet has two poles at its ends.
S
N
B is the magnetic field vector (magnetic flux
density)
Magnetic poles come in two types, “N” and “S”.
Due to the Earth’s magnetism, a magnet will tend to
rotate until the “N” end points North. (the earth’s
north magnetic pole is actually a south pole)
Forces between magnets are due to the forces
between each pair of poles, similar to the
electrostatic forces between point charges.
N
N
S
S
S
unlike poles attract
like poles repel
N
N
N
The force gets smaller as distance increases.
Magnetic Field B
Magnetic poles
produce a field B
(think of S as a – charge
and of N as a + charge)
The external
field exerts
forces on poles
N
S
F
F
N
S
B
B
Quiz
What is the direction of the force on a magnetic
dipole placed in a uniform magnetic field?
B
S
N
Magnetic field lines and Magnetic Dipoles
Compass needle (a magnetic dipole) aligns with B
B
compass
B
N
S
S
N
Lines point
out from N
pole
Electric charge and Magnetic fields
Hans Ørsted discovered (1819) that moving electric
charges create magnetic fields. Also, external
magnetic fields exert forces on moving electric
charges.
A current loop acts like a magnetic dipole.
Define B by the force that an external field
exerts on a moving charge:

Charge q moving with velocity v , feels a force

 
F  qv  B
(vector product)
F
B
q
+

v

 
F  qv  B
 
1) F  B
 
2) F  v  NO work done!

3) F  q v B sin
4) For a negative charge, the force is in the
opposite direction.
UNITS:
N
weber  Wb 
 tesla () 
 2
2
m
m
m 
C s
Also…
1 Gauss (G) = 10-4 T
Typical Fields
Earth’s Field
~ 1 x 10-4 T (1 Gauss)
Strong fridge magnet
~ 10-2 T (100 G)
Big lab electromagnet
~ 4 T (40,000 G)
Superconducting magnet
up to ~ 20 T
(200,000 G)
Vector Diagrams
The three vectors F, v, B never lie in a single plane,
so the diagrams are always three-dimensional. The
following convention helps with drawing the vectors.
For vectors perpendicular to the page, we use:
X
into the page (tail feathers of arrow)
out of the page (point of arrow)
Examples
For a positive charge q moving with velocity v:
draw the force vector.
x
x
x
x
x
x
x
x
x x
x x
x x B
x vx
B
v
v x
v
B
B
B
Wire
+
+
+
+
+
+
+
current I
L
Current I flows from left to right. In what direction
is the force on the wire?
B
+
+
+
+
+
+
+

L
The total force on the wire of length L is F = Nqv x B,
where N is the number of charges in length L.
N = (number of charges/volume) x (volume)
= n x (AL), where A is the cross-sectional area
So, F = (nALqv) x B
= (nqvA)L x B
or,
F=ILxB
(straight wire, uniform B)
The vector length L points along the wire in the
direction of the current.
Example
Assume the earth’s
magnetic field is 0.5 x 10-4
T, and points North, 50o
below the horizontal.
up
0.5 x 10-4 T
What is the force
(magnitude and direction)
on a straight horizontal
power line 100 m long,
carrying 400 A:
A) if the current is flowing North
B) if the current is flowing East
north
50o
Solution