Ch29 Magnetic Fields
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Transcript of Ch29 Magnetic Fields
Magnetic Field and Magnetic Force
vF ,qB
BvFF ,BB
0// BFBv
vBF ,0 B
vF ,0qB vF ,0qB
sinBF
B
v+q
FB
oppositedirection
Electric and Magnetic Forces
Electric forces act in the direction of the electric field, magnetic forces are perpendicular to the magnetic field.
A magnetic force exists only for charges in motion. The magnetic force of a steady magnetic field
does no work when displacing a charged particle. The magnetic field can alter the direction of a
moving charged particle but not it speed or its kinetic energy.
BvF qB EF qE
Magnetic Force on a Current Carrying Conductor Magnetic force acts upon charges moving
in a conductor. The total force on the current is the integral
sum of the force on each charge in the current.
In turn, the charges transfer the force on to the wire when they collide with the atoms of the wire.
Magnetic Force on a Current Carrying Conductor
BvF dqB q,
nALq dB BvF
qnAvI d
BLF IBFor a straight wire in a uniform field
BsF Idd B
b
aB dI BsF
For an arbitrary wire in an arbitrary field
Closed Loop in a Magnetic Field
BsF dIB
0 sd0BF
Net magnetic force acting on any closed current loop in a uniform magnetic field is zero.
Forces on a Semicircular Conductor
IRBILBF 21
On the straight wire
dsIBdIdF sin2 Bs
On the curved wire
RddsRs
dIRBdF sin2
00
2 sinsin dIRBdIRBF
IRBF 22
Directed out of the board
Directed in to the board
021 FFF
Torque on a Current Loop in a Uniform Magnetic Field
00
BFBL
For 1 and 3,
IaBFF 42
bIaB
bIaBbIaBbFbF
max
42max 2222
If the field is parallel to the plane of the loop
IABmax
For 2 and 4,
Torque on a Current Loop in a Uniform Magnetic Field
If the field makes an angle with a line perpendicular to the plane of the loop:
042 FF
sin
sinsin2
sin2
sin2
sin2 31
IAB
IabBaIbBaIbB
aFaF
BAI
Concept QuestionA rectangular loop is placed in a uniform magnetic field with the plane of the loop perpendicular to the direction of the field.If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop:
1. a net force.2. a net torque.3. a net force and a net torque.4. neither a net force nor a net torque.
Magnetic Dipole MomentAμ I
Bμ
(Amperes.m2)
If the wire makes N loops around A,
BμBμ coilloopN
Bμ U
The potential energy of the loop is:
Motion of Charged Particles in a Uniform Magnetic Field
Consider a positive charge moving perpendicular to a magnetic field with an initial velocity, v.The force FB is always at right angles to v and its magnitude is,
qvBFB
So, as q moves, it will rotate about a circle and FB and v will always be perpendicular. The magnitude of v will always be the same, only its direction will change.
Cyclotron FrequencyTo find the radius and frequency of the rotation:
rmaF
rvmqvBFB2
qBmvr
mqB
rv
qBm
vrT
222
The radial force
The angular speed
The period
Cyclotron frequency
Helical MotionIf the initial velocity makes an arbitrary angle with B,
vx = constantvy and vz change in timeThe resulting motion is a helix
The equations for the cyclotron frequency and rotation period still apply provided, 22
zy vvv
Concept QuestionCosmic rays (atomic nuclei stripped bare of their electrons) would continuously bombard Earth’s surface if most of them were not deflected by Earth’s magnetic field. Given that Earth is, to an excellent approximation, a magnetic dipole, the intensity of cosmic rays bombarding its surface is greatest at the
1. poles.2. mid-latitudes.3. equator.
Summary The right hand rule Magnetic forces on charged particles and
current carrying wires Torque on loops and magnetic dipole
moments Charged particle motion