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Certain iron containing materials have been known to attract or repel each other.
Compasses align to the magnetic field of earth.
Analogous to positive and negative charges, every magnet has a north and a south pole (but always as a pair).
Magnetic fields can be created by electrical currents.
FB


FB  q, v
B
+q

v

 
v // B  FB  0

 
  0  FB  B, v


FB q  0, v 
opposite
direction

FB  sin 


FB q  0, v 

 
FB  qv  B
FB  q vB sin 
Magnetic Field, B: Tesla (T)=N/(C.m/s)=N/(A.m)
Right Hand Rule
Magnetic Field
Representation

 
FB  qv  B


FE  qE
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 its speed or its kinetic energy.
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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,
FB  qvB
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.
To find the radius and frequency of the rotation:
The radial force
 F  ma
r
v2
FB  qvB  m
r
r
mv
qB
The angular speed  
v qB

r m
The period
2r 2 2m


v

qB
T
Cyclotron frequency
Electron beam in a magnetic field
V = 350 V
v
V
r
FB
B
K  U
1
me v 2  eV
2
r = 7.5 cm
q = e = 1.6 x 10-19 C
m = me = 9.11 x 10-31 kg
B=?
=?
v
r
mv
qB

2eV
 1.11107 m / s
me
B
me v
 8.4 10  4 T
er
qB eB

 1.5 108 rad / s
m me
Helical Motion –
vx, vy and vz
Cosmic Rays in the
Van Allen Belt
Complex Fields –
Magnetic Bottles
Essentially it is the total electric and magnetic force acting upon a charge.


 
F  qE  qv  B
Velocity Selector
Mass Spectrometer
Fe  FB
v
E
B
m rB0 B

q
E
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.
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


 
FB ,q  qv d  B



FB  qv d  B nAL


I  vd qnA

 
FB  IL  B
For a straight
wire in a uniform
field

 
dFB  Id s  B
b

 
FB  I  d s  B
a
For an arbitrary
wire in an
arbitrary field
b

 
FB  I  d s  B
a

 b  
FB  I   d s   B
a 

 
FB  IL  B
The net magnetic force acting on a curved wire in
a uniform magnetic field is the same as that of a
straight wire between the same end points.
 

 
FB  I  d s  B

 ds  0

FB  0
Net magnetic force
acting on any closed
current loop in a uniform
magnetic field is zero.
On the curved wire
 
dF2  I d s  B  IB sin ds
s  R
ds  Rd
dF2  IRB sin d


0
0
F2  2 IRB
Directed in to the board
F2   IRB sin d  IRB  sin d
On the straight wire
F1  ILB  2 IRB
Directed out of the board
  
F  F1  F2  0
If the field is parallel to the plane of the loop
 
LB  0
For 1 and 3, 
FB  0
For 2 and 4, F2  F4  IaB
 max
 max
b
b
b
b
 F2  F4  IaB   IaB 
2
2
2
2
 IaB b
 max  IAB
If the field makes an angle
with a line perpendicular
to the plane of the loop:
a
a
  F2 sin   F4 sin 
2
2
b
b
  IaB sin   IaB sin   IabB sin 
2
2
  IAB sin 
 

τ  IA  B
A 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.


μ  IA
(Amperes.m2)
  
τ  μB
If the wire makes N loops around A,
 



τ  Nμ loop  B  μ coil  B
The potential energy of the loop is:
 
U  μ  B
qvd B  qE H
E H  vd B
VH  vd Bd
vd 
I
nqA
IB RH IB
VH 

nqt
t
The right hand rule
Magnetic forces on charged particles
 Charged particle motion
 Magnetic forces on current carrying wires
 Torque on loops and magnetic dipole moments
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Reading Assignment
 Chapter 30 – Sources of the Magnetic Field
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WebAssign: Assignment 7