Download Lecture 8 Magnetic field

Magnetic Poles
 Every magnet, regardless of its shape, has two poles
 Called north and south poles
 Poles exert forces on one another


Similar to the way electric charges exert forces on each other
Same poles repel each other ; opposite poles attract each
other
 The force between two poles varies as the inverse
square of the distance between them
 Magnetic poles are always found in pairs
Magnetic Field
 The region of space surrounding any moving electric
charge also contains a magnetic field
 A magnetic field also surrounds a magnetic substance
making up a permanent magnet
 A vector quantity
 Symbol : B
 Direction is given by the direction a
north pole of a compass needle points
in that location
Magnetic Force
 The magnetic field can be defined in terms of
magnetic force
 The magnetic force
FB  qv  B

FB
 q


v
B
is the magnetic force
is the charge
is the velocity of the moving charge
is the magnetic field
Differences between E and B
fields
 Direction of force
 Direction of FE is along E , while direction of FB is
perpendicular to B.
 Motion
 FE acts on a charged particle regardless of whether the
particle is moving, while FB acts only on a moving
charged particle.
 Work
 FE produces work when acting on a charged particle,
while FB produces no work when acting on a charged
particle.
Units of Magnetic Field
 The SI unit of magnetic field is the tesla (T)
Wb
N
N
T 2 

m
C ( m / s ) A  m
 Wb is a weber
 A non-SI commonly used unit is a gauss (G)
 1 T = 104 G
Notation of Direction
 When vectors are perpendicular
to the page, dots and crosses are
used
 The dots represent the arrows
coming out of the page
 The crosses represent the arrows
going into the page
Charged Particle in a Magnetic
Field
 Consider a particle moving
in an external magnetic
field with its velocity
perpendicular to the field
 The force is always directed
toward the center of the
circular path
mv 2
FB  qvB 
r
mv
r
qB
More About Motion of Charged
Particle
 The angular speed of the particle is
v qB
ω 
r
m
 The angular speed, w, is also referred to as the cyclotron
frequency
 The period of the motion is
2πr 2π 2πm
T


v
ω
qB
Charged Particles Moving in
Electric and Magnetic Fields
 In that case, the total force is the sum of the forces due
to the individual fields
 In general: F  qE  qv  B
 Thomson’s e/m Experiment
Magnetic Force on a Current
Carrying Conductor
 A force is exerted on a
current-carrying wire
placed in a magnetic field
 The current is a
collection of many
charged particles in
motion
 The direction of the force
is given by the right-hand
rule
Force on a Wire, equation
 The magnetic force is
exerted on each moving
charge in the wire
 F  qv  B
d
 The total force is the
product of the force on
one charge and the
number of charges



F  qvd  B nAL
FB  IL  B
Torque on a Current Loop
 The rectangular loop carries a
current I in a uniform
magnetic field
 No magnetic force acts on
sides 1 & 3
 Force on sides 2 & 4 :
 F2 = F4 = I a B
 The area enclosed by the loop
is ab, so τmax = IAB
Torque on a Current Loop,
General

 IA  B where A is
perpendicular to the plane of
the loop and has a magnitude
equal to the area of the loop
Magnetic Dipole Moment
 The product IA is defined as the magnetic dipole
moment, , of the loop
 Often called the magnetic moment
 SI units: A · m2
 Torque in terms of magnetic moment:
   B
 Analogous to 
 p  E for electric dipole
Potential Energy
 The potential energy of the system of a magnetic
dipole in a magnetic field depends on the orientation
of the dipole in the magnetic field:
U   B
 Umin = -B and occurs when the dipole moment is in the
same direction as the field
 Umax = +B and occurs when the dipole moment is in the
direction opposite the field