1. Magnetism
Physics 122
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Lecture XII

2. Magnetic force on moving charge
Magnetic force F is perpendicular to the velocity v of a particle with charge q
F=qvB sin q
Magnetic field does not change the magnitude of particle’s velocity, only its direction. Charged particles move in circles in constant magnetic field
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Lecture XII

3. Magnetic force on moving charge
Circular motion
Magnetic force = Centripetal force
F=qvB
Centripetal acceleration
a=v2/R
Newton’s second law
F=ma
qvB=mv2/R
In experiments B is known,
q=e most of the time,
Measure R- measure mv
For a given v measure m – magnetic spectrometer
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Lecture XII

4. Cyclotron frequency Frequency does not depend on v!
For a given particle type (q,m=const) it depends only on B
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5. Particle selector + Crossed E and B fields:
For one given velocity electric force exactly compensates magnetic force
Only particles with this value of velocity emerge from particle selector +
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6. Crossed fields
Electric field changes kinetic energy of charged particle
qDV=mv2/2
Magnetic field does not change KE, only direction
Lorentz force:
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7. Torque
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8. Current loop in magnetic field
A=ab – area of the loop
Magnetic field exerts a torque on a loop parallel to the magnetic field:
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9. Current loop in magnetic field
q – angle between magnetic field and a perpendicular to the loop !!!
Magnetic field orients a loop current perpendicular to B.
N loops:
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10. Magnetic moment
Current loop (area A, current I, number of turns N) in constant magnetic field B experiences torque
Define magnetic moment m perpendicular to the plane of the loop
Torque
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11. Magnetic moment
Equilibrium position for current loop is when B is perpendicular to the face of the loop, or when magnetic moment is parallel to B
Inside magnetic field magnetic moments orient parallel to the field
Galvanometer: B is know – measure I
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Lecture XII

12. Magnetic field created by currents
Electric currents – moving electric charges - create magnetic field
Stationary electric charges do not create magnetic filed
First right hand rule
Thumb along the current
Wrap your fingers around the wire
fingers show the direction of the magnetic field
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Lecture XII

13. Magnetic field created by current
Magnetic field B created by current I at a distance r from the conductor is
m0 = 4p 10-7 Tm/A- magnetic permeability of free space
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14. Ampere’s Law In a way similar to Gauss’s law for E and Q
Not flux, integral over closed path
Only component of B parallel to dl contributes to integral
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15. Application of Ampere’s Law
Thick wire of radius R carries current I. What is B(r ) in and outside of the wire?
Current through unit area:
Current through circle radius r<R
Path integral over radius r
Ampere’s law
For r>R – same as thin wire
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16. Practical application: coaxial cable
Cylindrical braid carries return current  magnetic field outside is zero.
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Lecture XII