1.moving electric charges produce magnetic fields, b b measured in tesla (1t = 10 4 gauss) earth’s...
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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
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Magnetic Force
• F = qvB if v ┴ B• F = 0 if v ║ B• F = qvB sin, if v makes angle with B• Right hand rule for direction
• In case where v ┴ B, the trajectory is a circle
• In general, the trajectory is a helix
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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
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Forces & Torques on a Current Loop
w
B
F
F
r = (w/2)sin
=IA X
In general, = B sin, where is the angle between (perpendicular to the area) and B
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I
r
B
B
BI
ro
2
,
Right Hand Rule
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Group Problem
• A long straight wire lies along the x-axis and has a constant current of 3A in the + direction.
a) Find B at a point 2m from the wireb) Find B at a point 1.5 m from the wire in the opposite
direction from (a)c) 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.
d) 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
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