Transcript 08EM3_Magnetism

How Do Magnets Behave?
• A Magnet has two poles: “North” and “South”. Example:
The Earth.
• For two magnets:
–Unlike poles attract; like poles repel.
• The North Pole of a magnet points North (towards the
Arctic) by definition.
•Where is Earth’s South Pole?
–In Canada.
•Where is Earth’s North Pole?
–In Antarctica.
•Magnetism acts through a Magnetic Field
(a “ B-field ”) (S.I. Unit: “Tesla” (T))
How can we Visualize Magnetic Fields?
• Magnetic Field Lines
– Lines start at North Pole and end at South Pole.
– Lines must have a start and end; a North Pole cannot
exist without a South Pole.
– Direction of a line at a point is in the direction of
the B-field.
– Density of lines is proportional to the magnetic field
strength.
– Patterns Similar to E-field lines can be found:
• Magnetic Dipole
• Repulsive poles
• Magnetic Quadrupole.
How is Magnetism caused?
• Magnetism is
– caused by moving charges.
– felt by moving charges.
• The charges must be moving to cause or be affected
by magnetism.
• A stationary charge will cause and feel an E-field.
• A moving charge will cause and feel an E-field and
a B-field.
• Electric Currents (moving charges)
– Cause B-Fields (Hans Oersted, 1820)
– Feel B-Fields
Questions?
• But isn’t a charge’s motion relative to an
observer?
– The magnetic and electric fields observed depend
on your reference frame.
• What about magnets? Where are their moving
charges?
B-Fields caused by Currents
• A current causes a B-field that is perpendicular to current
flow.
• Point your right thumb in the direction of the current; your
fingers will curl in the direction of the B-field. (“Right
Hand Rule #1”).
Forces between Current Carrying Wires.
Wires with currents in the
same direction attract.
The opposite B-fields
between the wires are
as two unlike poles.
Wires with currents in
opposite directions repel.
The B-fields between the wires
are in the same direction and
are as two like poles.
Magnitude and Direction of Force on a
Current Carrying Wire due to a B-Field
• Magnitude: For a Wire having
current I and length (l ) making
an angle (θ) with the B-field:
FB = I l B sin θ
• Direction:
– Right Hand Rule #2
– Thumb in direction of Current.
– Fingers in direction of B-Field.
– Palm points to direction of
Force.
NOTE: FB is
PERPENDICULAR TO
BOTH I and B.
Examples
1. Verify Right Hand Rule #2 For these
wires.
2. Suppose the current in a wire is in the
same direction as the B-Field. In what
direction is the Force?
Answer: The Force is zero because sin θ is zero.
Magnitude and Direction of Force on a Charged
Particle due to a B-Field
• Suppose we follow one charged (+q) particle in a
current:
– Particle has velocity (v) in the direction of the
current.
– In time (Δt) the charge covers a distance: l= vΔt
• Thinking of one charged particle as a small
current, the force is
FB = IlB sinθ = (q/Δt) (vΔt) B sinθ
• Magnitude: FB = qvBsinθ
• Direction: Use RHR#2 with v instead of I
Examples
1. A wire of length l =.12 m and current I =30A
makes an angle of 60o with a B-field having a
magnitude of .90 T in the x-direction as shown.
What is the Force on the wire?
I
θ
B
Examples (cont’d)
2. A square wire loop has a mass m = 0.5kg and a
current I=10.0A. The loop hangs from a spring
scale measuring in newtons. If the bottom of the
loop is in a uniform B-field of 0.5T coming out of
the page, what is the reading on the spring scale?
Examples (cont’d)
3. A positron (charge: +e) enters a region of
uniform magnetic field of B = .10T directed
into the page. The positron’s initial velocity is
v =106m/s in the +x direction.
a. What path does the particle follow?
b. What is the rate at which work is done on the
particle by the B-field?
c. How would the path change if the particle were an
electron?
d. How is this scenario used by particle physicists?
Examples (cont’d)
4. Mass Spectrometer:
Using Applied Electric and Magnetic Fields to
find a particle’s mass (see pg. 642 of text):
Northern Lights
(Example 5)
Magnetic Field due to a Long Wire
(WITHOUT PROOF)
Magnetic Permeability of Free Space:
Force Between Two Wires Carrying Current
L
d
Force on wire 1 by wire 2: F1 = I1 B2 (to the right)
Force on wire 2 by wire 1: F2 = I2 B1 (to the left)
(So the wires attract)
Magnetic Fields of Loops, Coils, and
Solenoids
(WITHOUT PROOF)
• For a wire loop of radius (r) carrying a current
(I), the B-field at the center of the loop is:
B = (μ0 I)/2r
• For a coil of N-loops of radius (r):
B = (μ0 N I)/2r (WHY?)
• For a solenoid of N-loops and length (L):
B = (μ0 N I)/L
(WHY?)
or: B = μ0 n I ; n = N / L
Convenient Alternate RHR1 for
Loops, Coils, and Solenoids
Curl your fingers in the direction of the current
then thumb points in the direction of the B-field.
How do Magnetic Materials cause
B-fields?
• Electrons in atoms have “spin”; an intrinsic fixed
quantity of angular momentum.
– Spin can be “up” (+) or “down” (-)
– Unpaired electrons in atom give the atom a net spin.
• A net spin (rotational vector)
– acts an effective current associated with the atom.
– The spin and B-field of current are the same.
• If all atoms have their spins in same direction
– An effective BOUND surface current exists and ….
– the material is magnetic
Magnetic Materials (cont’d)
Nonmagnetic
Material
(spins randomly
directed)
Permanent
Magnet
(spins aligned)
Ferromagnetism
• A ferromagnetic material
has magnetic domains,
regions in which spins line
up, but domains cancel on
average.
• Applying an external Bfield causes the domains to
line up and the sample
becomes a magnet.
(Example: electromagnet)
Magnetic Materials (cont’d)
• Permanent Magnet- Spins aligned on
neighboring atoms (“ordered”), appears magnetic.
• Nonmagnetic – Spins randomly distributed;
B-fields cancel out on average.
• Antiferromagnet – Spins on neighboring atoms
aligned in opposite directions (“ordered”);
B-fields cancel locally.
A
Magnetic Flux
• Magnetic Field Strength (B):
– S.I. Unit: Tesla (T)
– Proportional to density of field lines
• Magnetic Flux (Φm)
– Φm = (B┴ × A) = BAcos(θ)
– Proportional to number of field lines
through an area.
– S.I. Unit: Weber (Wb) (1 Wb = 1T×m2)
B
Electromagnetic Induction
• Faraday’s Law:
– Emf = ε = - (Δ Φm )/Δt
– For a coil of N loops: ε = -N (Δ Φm )/Δt
– Lenz’s Law: The current and emf induced
by the changing magnetic flux is in a
direction so as to oppose the change in
flux.
Applications
1. Motional emf : A conducting rod rides on
conducting rails with velocity (v) to the right
as shown, in a uniform magnetic field as
shown. Given B, L, and v, what is the emf
generated?
Motional Emf Applet
Applications (cont’d)
2. Electric Generators: How power companies
generate electricity for cities and homes.
•
•
•
Relative motion of magnet and coil is what
produces emf.
Moving a magnet in and out of a coil produces an
alternating current.
Rotating a loop (or coil) between the poles of a
magnet causes AC.
Electric Generators (cont’d)
• Current is induced in lower and upper sides of the wire loop.
•Upper side has v coming out of board, resulting in a current
to the right.
•Lower side has v going into the board, resulting in a current
to the left.
•Currents add to cause clockwise current.
•
Electric Generators (cont’d)
• Angle of Area Vector and B-field fluctuates
between θ = 0° and 180 °
• Current and emf reverses direction with
angular frequency (ω): θ = ωt
• ε = - (Δ Φm )/Δt = -BA Δ(cos (ωt))/ Δt
= BA ω sin (ωt) (using calculus)
You are not responsible for this formula; just the
concept of how AC is produced.
Result: Alternating Current (AC)
Power Generation
• Fuel (Nuclear, coal, water, wind) is used to create
steam
• Steam drives a turbine.
• The turbine rotates a coil of wires between a the
poles of a strong magnet.
• Alternating Current is produced
• Faster Rotation causes larger current.
• AC produced is carried to cities and homes.
The Big Picture of Electrical
Power Creation
The Big Picture of Electrical
Power Delivery
Transformers (Devices with Two Coils):
Used to adjust Voltage/Current Characteristics
Power is conserved: P = VHIGHILOW = VLOWIHIGH
Power is Transmitted more efficiently at: VHIGHILOW
E&M
• A changing E-field (or voltage) causes a changing
B-field.
– We saw this with an electromagnet.
• A changing B-field causes a changing E-field (or
voltage)
– We saw this by moving a magnet in a coil
• Maxwell’s Equations:
– Four equations summarizing Classical Electrodynamics
• Electromagnetic Waves:
– Transfer Electric and Magnetic energy (Radiation)
– Have oscillating E-fields and B-fields.
Maxwell’s Equations:
E&M Summarized