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Ampere’s Law
Physics 102
Professor Lee Carkner
Lecture 19
PAL #18 Magnetic Force
How long would it take an electron to
complete one circular orbit around a 1 G
magnetic field?

Distance around circle is circumference:
Can find velocity from equation:
v = rqB/m
t = (2pr)/(rqB/m) =
t = [(2)(p)(9.1X10-31)]/[(1.6X10-19)(1X10-4)]
t =
Currents and Magnetism

It is also true that moving charged
particles produce magnetic fields

Serious magnetic fields are produced by
currents
What is the magnitude and direction of
these fields?
Magnetic Field from a Current
in a Wire

Needle deflected tangentially to the
wire cross section

How can we find the direction and
magnitude of the B field for any
situation?
Right Hand Rule Revisited
Grasp the wire with
your thumb in the
direction of the current
and your curled
fingers indicate the
direction of the field

Ampere’s Law
To find the magnitude of the B field we use
Ampere’s law

The sum of the product of DL and B around
the entire path is equal to m0I

We can express Ampere’s law as:
S BDL = m0I
B Field for a Wire
Use Ampere’s law for a circle of radius r around the
wire
Since B is the same everywhere around the circle

B 2pr = m0I
Magnetic field a distance r from a long straight wire with
current I
Today’s PAL
I
I
Consider two parallel metal
rails 1 cm apart and each
carrying 100000 A of current in
opposite directions
What is the direction and
magnitude of B at a point
halfway in-between them?
What is the direction and
magnitude of the force on a
conductor also carrying 100000
A that connects the two rails?
Force on Two Parallel Wires

The B field then will exert a force on the
other wire
F = BIL = m0IIL/2pd

F = m0I1I2L/2pd
Magnetic Field: Loop

Can apply the right
hand rule all the way
around

Loop acts as a bar
magnet
Magnetic Field: Solenoid
What happens if you
stack several loops up?

You produce a
solenoid

Field inside the
solenoid is strong and
uniform (far from the
ends)
Electromagnet
We can write an expression for the
solenoid magnetic field:
B = m0nI

If you put a piece of iron in the center
you get an electromagnet

Next Time
Exam #2
Same format as Exam #1
Covers chapters 16-20
Practice problems posted on
WebAssign
Will not count for grade
Reading and homework for Monday on
webpage