Download Phy 211: General Physics I

Phy 213: General Physics III
Chapter 28: Magnetic Fields
Lecture Notes
Magnetic Fields
• The movement of electric charge produces a magnetic (B) field
• A single magnetic point charge (called a magnetic monopole) has never
been discovered in nature
• Magnetism always exists as a dipole never as a point “charge”
• Magnetic materials have both north and south poles
• Magnetic field lines point from North (N) to South (S)
N
• The units of magnetic field are called Tesla (T)
1 Tesla (T) = 1 N.s/C.m
S
The Earth as a Magnet
• The Earth has a magnetic field and acts like a big magnet
• We define the magnetic “north” direction as the direction the
North end of a compass points
– The geographic “North Pole” is really
the South pole of the magnetic field
– The geographic “South Pole” is really
the North pole of the magnetic field
• Although its value varies
depending on location, the
magnitude of the Earth’s
magnetic field is ~ 6x10-5 T
Magnetic Fields (moving charges)
• Moving charges produce magnetic fields
• The magnitude of the produced magnetic field depends:
– Magnitude of charge (q)
– Speed of the charge (v)
– Distance from charge (r)
• Direction of magnetic field is determined by the “right hand
rule”
– Point thumb in direction of v (or –v for negative charge)
– Curl fingers around the thumb
– The direction of the fingers is the direction of magnetic field
Examples: What is the direction of the B field?
+
v
-
v
Magnetic Force
• Magnetic fields exert force on moving
charges (the magnetic force)
• The direction of the magnetic force is
– Perpendicular to the direction of movement
– Perpendicular to the direction of magnetic
field
• The magnetic force exerted on a charge
depends on:
–
–
–
–
The magnitude of the moving charge (q)
The speed of the moving charge (v)
The magnitude of the magnetic field (B)
The angle (q) between v and B
• To calculate magnetic force on a moving
charge:
FB = qv  B
or
FB = qvB  sinq
Magnetic Force on a Current-Carrying Wire
• Current carrying wires have moving charge
• When placed in a magnetic field, the field can exert a force
on these moving charges
• The magnetic force vector exerted on a current carrying wire
of length, L, is:
FB = iL B
• The magnitude of the magnetic force vector:
• Example:
FB = iLB  sinq
FB
B
L
i
The Hall Effect
• When a perpendicular magnetic
field is applied to a current
carrying material, the charge path
becomes curved with moving
charge accumulating on one face
of the material & equal and
opposite charges exposed on the
other face.
• The separation of charge
establishes an electric field that
opposes the migration of further
charge, and an electrical potential
builds up for as long as the
current is flowing.
e-
-
+
i
VHall
B
Torque Exerted on a Current Loops
• Although the net magnetic force exerted on a current carrying
loop in a magnetic field is zero, the field does exert torque on
the loop
• Consider a square loop (length of sides = L and current = i) in
a constant magnetic field:
• On 2 sides of the loop, FB =0
• For each of the other sides, FB= iLB is pointing opposite
directions
• Each of these forces exerts a torque on the loop:
L 
FB
 FB1 = FB2 =  FB=   iLB  sin
B
2
L
• The net torque on the loop is:
Net=F +F =iL2B  sin= iAB  sin
B1
B2
• When there are N loops:
i
 Net=NiA B  sin
FB
Magnetic Moment
• The quantity NiA is referred to as the
magnetic moment vector (m) for the loop
• The direction of is the normal vector to the
face of the loop:
m =NiAiˆN
• The torque on the loop can then be
expressed (for any N, A, and i) as:
 Net =NiA  B  sin
 Net =NiAiˆN  B= m  B
• The magnetic potential energy is given by:
U q =-m  B
m
i
B
Magnetic Force in DC Motors
• A simple DC motor is comprised of a rotating wire coil (called
an armature) connected to a battery (or DC power source)
• The armature is placed within a between the opposite poles
of 2 magnets
• As current passes along the coil, the magnetic field exerts
force on the wires generating torque that results in the
rotation of the armature
• As it rotates, the magnitude
of torque (force) acting on
the armature depends on its
orientation in the magnetic
field