magnetism
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Magnetism. Physics 122. Magnetic force on moving charge. Magnetic force F is perpendicular to the velocity v of a particle with charge q F=qvB sin q - PowerPoint PPT PresentationTRANSCRIPT
04/19/23 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
• Magnetic field does not change the magnitude of particle’s velocity, only its direction. Charged particles move in circles in constant magnetic field
vF
BvqF
04/19/23 Lecture XII 3
Magnetic force on moving charge• Circular motion • Magnetic force =
Centripetal forceF=qvB
• Centripetal acceleration a=v2/R
• Newton’s second lawF=maqvB=mv2/R
qB
mvR
In experiments B is known,q=e most of the time, Measure R- measure mvFor a given v measure m – magnetic spectrometer
04/19/23 Lecture XII 4
Cyclotron frequency
qB
mvR
vTR 2 :circle full
Bm
q
Tf
qB
mT
vTqB
mv
2
1
2
2
Frequency does not depend on v!For a given particle type (q,m=const) it depends only on B
04/19/23 Lecture XII 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
BvqEqF
+ + + +
- - - -
+
BvqEqF
B
Ev
BvqF
EqF
v
04/19/23 Lecture XII 6
Crossed fields
• Electric field changes kinetic energy of charged particle
qV=mv2/2
• Magnetic field does not change KE, only direction
• Lorentz force:
BvqEqF
04/19/23 Lecture XII 8
Current loop in magnetic field
IaBF 1
IaBF 2
211
bF
222
bF
IABIabB
bIaB
bIaB
22
21
IAB
• A=ab – area of the loop• Magnetic field exerts a torque
on a loop parallel to the magnetic field:
04/19/23 Lecture XII 9
Current loop in magnetic field
– angle between magnetic field and a perpendicular to the loop !!!
• Magnetic field orients a loop current perpendicular to B.
• N loops:211
bF
222
bF
IAB
2sin11
bF
2sin22
bF
sinIAB
sinNIAB
04/19/23 Lecture XII 10
Magnetic moment• Current loop (area A, current I,
number of turns N) in constant magnetic field B experiences torque
• Define magnetic moment perpendicular to the plane of the loop
• Torque
NIAB
ANI
B
NIAB
04/19/23 Lecture XII 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
BBU
cos
04/19/23 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
04/19/23 Lecture XII 13
Magnetic field created by current
• Magnetic field B created by current I at a distance r from the conductor is
Tm/Amagneticpermeability of free space
r
IB
2
0
04/19/23 Lecture XII 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
enclIldB 0�
04/19/23 Lecture XII 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
20
2
2
00
2)(
2
R
IrrB
R
rIIrB encl
rB 2
2
2
R
rI
2R
I
20
2
2
00
2)(
2
R
IrrB
R
rIIrB encl
r
IrB
2
)( 0