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1. Moving electric charges produce
magnetic fields, B
B measured in Tesla (1T = 104 Gauss)
Earth’s B field ~ 0.5 Gauss
Largest permanent magnet ~ few T
Largest man-made magnet ~ 20 T
2. Magnetic fields exert forces on moving
electric charges
Magnetic Force
•
•
•
•
F = qvB
if v ┴ B
F=0
if v ║ B
F = qvB sinq,if v makes angle q with B
Right hand rule for direction
• In case where v ┴ B, the trajectory is a
circle
• In general, the trajectory is a helix
Group Problem
•
Suppose a proton has a velocity v = 106
m/s to the right perpendicular to a
uniform magnetic field B = 2 T (take B
directed up out of the paper ).
a) What is the force on the proton?
(magnitude and direction )
b) What will be the path of the proton?
c) Find the radius of the circular orbit of the
proton
Forces & Torques on a Current
Loop
B
=IA q
w
X
F
r = (w/2)sinq
F
In general, t = B sinq, where q is the
angle between (perpendicular to the
area) and B
I
B
r
B
o I
B
,
2 r
Group Problem
•
a)
b)
c)
d)
A long straight wire lies along the x-axis and has a
constant current of 3A in the + direction.
Find B at a point 2m from the wire
Find B at a point 1.5 m from the wire in the opposite
direction from (a)
Find the force on an electron located at the point in (a)
and moving with a velocity of 3 m/s perpendicularly
away from the wire.
Find the force/length on a second long straight wire
lying parallel to the first 3 m away and having a current
of 2A in the opposite (-) direction