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Chapter 33
The Magnetic Field
L.A. Bumm
Mid-Term Exam 2
Wed (30 Mar) Evening 8-10pm
• Please use the MT2 conflict form on D2L if you absolutely
cannot be take the midterm at that time.
• Remember that a late start is OK and preferred—but fill out
the form so we will expect you.
• Please get the forms to me by Friday (25 Mar).
Magnetic Force Interactions
This is similar to what we observed for electric forces.
Electric Force: Like charges repel opposite charges attract
Magnetic Force: Like poles repel
opposite poles attract
Magnetism has no equivalent of charge—
always dipole
Magnetic monopoles, if they existed, would be analogous to positive and
negative charges. However magnetic monopoles have never been observed,
although they are predicted by some theories.
Magnetic Field lines
We draw lines of magnetic field.
• Magnetic Field lines:
run from North to South
• Always form closed loops
because there is no
equivalent of charge
What we call the north pole of a magnet is
better termed the north seeking pole
Magnetic Field from a Current Carrying Wire
An electric current creates a magnetic field around the wire.
Without current: The
compass needles simply
point north.
With current: The compass
needles are tangent to a
circle around the wire.
Right hand rule
The magnetic field B has the properties:
• A magnetic field is created at all points in space around a current-carrying wire.
• The magnetic field at each point is a vector. It has both a magnitude (magnetic
field strength, B) and direction.
• The magnetic field exerts forces on magnetic poles. The force on a north pole is
parallel to B; the force on a south pole is opposite to B.
Looking at Vectors
Tip of the arrow
vector field point out of the page

Tail of the arrow
vector field point into of the page
Magnetic Torque on Compass Needle
S
N
It can be helpful to remember that B
points from north to south.
So the north end of the compass
needle will want to point to the south
pole of the magnet and vice versa.
Current-Carrying Wire
2D view looking along wire with current pointing into the page
compass alignment
magnetic field lines
3D view showing
the magnetic field lines and
the magnetic field vectors.
magnetic field vectors
Clicker Question
A magnet on a pivot is free to rotate. It is placed in a uniform
magnetic field pointing to the right as shown.
Which way will it turn? Which way will it point?
Biot-Savart Law
Fundamentally currents are moving charges
The Biot-Savart Law describes the
magnetic field from a moving charge.
This is as fundamental an equation as the
electric field from a point charge.
B
0 qv  rˆ
4 r 2
SI unit of the magnetic field is the Tesla, abbreviated T.
Coulombs Law and other electric equations contain the proportionality constant ε0.
Magnetic equations contain the proportionality constant μ0.
magnetic: permeability of free space
electric: permittivity of free space
0  4 107 T m A –1
 0  8.85 1012 C2 N 1 m 2
Biot-Savart Law
Fundamentally currents are
moving charges
The Biot-Savart Law describes the
magnetic field from a moving charge.
This is as fundamental an equation as the
electric field from a point charge.
B
0 qv  rˆ
4 r 2
Direction of B
The cross product v  r̂ shows that the magnetic field is mutually perpendicular to the
velocity of the charge an the line between the charge and the point in space.
The sign of the charge is also important. A moving negative charge produces a B in the
opposite direction to a positive charge moving in the same direction.
Magnitude of B
The magnitude of B is proportional to q and v and the invers square of r.
Cross Product Review
The cross product of C into D.
C D
Direction of the cross product:
The direction of the cross product is always mutually perpendicular to both
vectors. Thus perpendicular to the plane containing both vectors.
Use the right hand rule to determine the direction, up or down.
• Align your fingers in the direction to rotate C into D.
• Your thumb points in the direction of the cross product.
Often we say “The cross product of C into D” to emphasize the order of the
cross product because that determines the direction.
C  D  D  C
The magnitude of the cross product:
|C × D| is proportional to the sine of
the angle between the vectors.
C  D  CD sin 
Stop here