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The force on a charge q moving with a velocity F
v
)( BvEqF
The magnitude of the force
sinqvBF
sec)//(][ meterCoulombNewtonsB
gausssmCNewtonmwteslaT 42 10//1/1)(1
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qvBFBv
amF
0 FmaF rr
r
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22 ri
qB
mvr
The angular velocity
m
qB
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r
v
0|| FBv
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Using Crossed and Fields E
B
Velocity selector
0 qEqvB
vBE
B
Ev independent of the mass of the particle!
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Mass spectrometer
qB
vmR 1
1
B
Ev
21
1 qB
EmR
22
2 qB
EmR
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Thomson’s e/m experiment
1897: Cavendish Laboratoryin Cambridge, England
m
eVveVmv
2
2
1 2
B
Ev
2
2
2
2
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E
m
e
m
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E
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Electron motion in a microwave oven
A magnetron in a microwave oven emits electromagnetic waves with frequency f=2450 MHz. What magnetic field strength is required for electrons to move in circular paths with this frequency?
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Exercise 1
An electron, q=1.6 10-19C moves with velocity
ondpermetersiniiv yx sec104106 55
It enters a magnetic field with What is the force on the electron?
2/1.0 mwebersiB x
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Problem 5
Hall effect: The magnetic force on the charge carries in a wire can be used to determine their sign. Show that there will be an electric field, set up inside a wire in a magnetic field, that is perpendicular to the direction of the current. You should be able to show that the sign of the field depends on whether the mobile charges are positive or negative.
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nAq
iv
qvBqEHall
nq
jB
nAq
iBEHall
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You place a slab of copper, 2.0 mm thick and 1.5 cm wide, in a uniform magnetic field with magnetic field with magnitude 0.40 T. When you run a 75-A current in the +x direction, you find by careful measurement that the potential at the left side of the slab is 0.81V higher than at the right side of the slab. From this measurement, determine the concentration of mobile electrons in copper.
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Exercise 3
A wire of length l and mass m is suspended as shown. A uniform magnetic field of magnitude B points into the page. What magnitude and direction would a current, passing through a wire, have to have so that the magnetic and gravitational forces would cancel?
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Problem 4
A metal wire of mass m can slide without friction on two parallel, horizontal, conducting rails. The rails are connected by a generator which delivers a constant current i to the circuit. There is a constant, vertical magnetic field, perpendicular to the plane of the rails. If the wire is initially at rest, find its velocity as a function of time.
i
B
lgenerator
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Current carrying wires1820 Hans Christian Oersted
Hans Christian Ørsted
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qB
mvr
The angular velocity
m
qB
qBmvv
r
v
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Uniform magnetic field, Bv
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Uniform , B
Bv
When a charged particle has velocity components both perpendicular and parallel to a uniform magnetic field, the particle moves in a helical path. The magnetic field does no work on the particle, so its speed and kinetic energy remain constant.
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Example: A proton ( ) is placed in the uniform magnetic field directed along the x-axis with magnitude 0.500 T. Only the magnetic force acts on the proton. At t=0 the proton has velocity componentsFind the radius of the helical path, the angular speed of the proton, and the pitch of the helix (the distance traveled along the helix axis per revolution).
kgmC 2719 1067.1,1060.1
./1000.2,0,/1050.1 55 smvvsmv zyx
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Ampere’s Law
irdB 0
The field produced by an infinite wire
a
iB
2
0
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The Field Produced by a Straight Wire
a
iB
2
0