Magnetism
Physics 114
7/24/2016
Lecture VII
1
Concepts
• Magnetic field
• Magnetic force
7/24/2016
Lecture VII
2
Skills
• Determine the direction of magnetic field
created by electric current
• Determine the direction of magnetic force on
electric current
• Two right hand rules
7/24/2016
Lecture VII
3
Magnets
• Magnets have magnetic
poles – north and south
– Like poles repel
– Unlike poles attract
• Similarity to electric
interaction
7/24/2016
Lecture VII
4
Magnetic field
• Introduce magnetic field:
– Field lines go from north pole to south
– Mnemonic rule – birds fly from north to south
7/24/2016
Lecture VII
5
Magnetic field of the Earth
• Earth has a magnetic field
B~5x10-5 T
• Compass - a small magnet in a
form of an arrow - is used to
determine the direction of the
magnetic field
• South magnetic pole is located
close to the north geographic
pole, that is why north end of
the compass is pole is pointing
there (unlike poles attract)
7/24/2016
Lecture VII
6
Magnetic field
• Magnetic field is labeled by B
• It is measured in Tesla and Gauss
1T=10 kG
1T=1N/A m
7/24/2016
Lecture VII
7
Magnets
• North and south poles do
not exist separately!!!
– two halves of a broken
magnet still have south and
north pole each
• Different from electric
charges – positive and
negative charges can exist
separately
7/24/2016
Lecture VII
8
Magnetic field created by currents
• Electric currents – moving electric charges - create magnetic field
• Stationary electric charges do not create magnetic field
• First right hand rule
– Thumb along the current
– Wrap your fingers around the wire
– fingers show the direction of the magnetic field
7/24/2016
Lecture VII
9
Magnetic field created by current
• Magnetic field B created by current I at a
distance r from the conductor is
m0 I
B=
2p r
m0 = 4p 10-7 Tm/A- magnetic permeability of free
space
7/24/2016
Lecture VII
10
Magnetic field of loop current
• Magnetic field is in ~ same direction inside a
current loop
• Several loops create stronger magnetic field solenoid
7/24/2016
Lecture VII
11
Magnetic field of a solenoid
• Magnetic field inside solenoid
– Is parallel to its axis
– Depends on the current I
– Depends on the number of loops per unit length n=N/l:
B=m0nI
– Does not depend on diameter
– Does not depend on the total length
7/24/2016
Lecture VII
12
Magnetic force on electric currents
• Magnetic field exert a magnetic force on electric currents –
moving electric charges
F=IlBsinq
q- angle between B and I
F is max when B is perpendicular I and zero when B is parallel to I
7/24/2016
Lecture VII
13
Direction of the magnetic force
•
•
•
•
Second right hand rule:
Fingers along the current
Bend to show the direction of the magnetic field
Thumb shows the direction of the force
7/24/2016
Lecture VII
14
Magnetic force on moving charge
• Magnetic force F is
perpendicular to the
velocity v of a particle
with charge q
F=qvB sin q
• Charged particles
move in circles in
magnetic fields
7/24/2016
Lecture VII
15
Magnetic fields are used to
separate matter from antimatter
And measure particle velocity
Bubble chamber picture
7/24/2016
Lecture VII
16
Torque
 = r F = Fr sin q
 = rF = rF sin q
7/24/2016
Lecture VII
17
Current loop in magnetic field
 = 1   2 =
b
b
= IaB  IaB =
2
2
= IabB = IAB
F1 = IaB
F2 = IaB
7/24/2016
b
 1 = F1
2
b
 2 = F2
2
• A=ab – area of the loop
• Magnetic field exerts a torque
on a loop parallel to the
magnetic field:
 = IAB
Lecture VII
18
Current loop in magnetic field
b
 1 = F1
2
b
 2 = F2
2
b
 1 = F1 sin q
2
b
 2 = F2 sin q
2
 = IAB
 = IAB sin q
7/24/2016
Lecture VII
 q – angle between
magnetic field and a
perpendicular to the
loop !!!
• Magnetic field orients
a loop current
perpendicular to B.
• N loops:
 = NIAB sin q
19
Force between two currents
• Parallel currents attract
• Anti-parallel repel
m 0 I1
B1 =
2p L
F21 = I 2lB1
l
m 0 I1 I 2 l
F21 =
2p L
7/24/2016
Lecture VII
20
Ferromagnetism
• Electrons inside atoms –
little loop currents
• When placed inside
magnetic field
microscopic currents
orient to enhance the
external field
• This effect happens only
in some materials –
ferromagnetic, e.g. iron.
7/24/2016
domains
Lecture VII
21
Magnetic materials
• Ferromagnetic Km>>1 (~1000)
– Iron, cobalt, nickel, some aloys
residual magnetism can be destroyed (orientation of the
domains randomized) by mechanical shock or high T
• Paramagnetic Km>1 just a bit (1+10-4,-5)
– No domains, but molecules have magnetic moment
– Aluminum, magnesium, oxygen, platinum
• Diamagnetic Km<1 a really tiny bit (1-10-5,-6)
– Molecules do not have a magnetic moment
– Copper, diamond, gold, silicon, nitrogen
7/24/2016
Lecture VII
22