Magnetic Fields Produced by Currents
Magnets produce forces on other magnets
Magnets produce forces on moving charged particles
Magnetic field produced by current in
a long straight wire
Magnitude:
Magnets produce forces on current-carrying wires & loops
Can moving charges create magnetic fields???
µ0 I r = radial distance from wire
2πr
µ0 = 4π × 10−7 T ⋅ m/A
B=
Direction: RHR #2:
Current Exerts Magnetic Force on Moving
Charge See Example #7
• Current produces magnetic field B
B =
0 I
2 r
• Get direction of B from RHR #2
• This B exerts a force on
moving charged particle q0
F = q0 vBsin
• Get direction of F from RHR #1
A long straight wire carries current I out of the page.
An electron moves towards the wire from the right.
What is the direction of the force on the electron?
.
v
A) Up
B) Down
C) Into the page
D) Out of the page
E) Some other direction
e-
Magnetic Forces Between Two
Current-Carrying Wires
• Currents in same direction:
• Currents in opposite directions:
See Example #8
Ex. Two 0.85 m rods of mass 0.073 kg are
oriented parallel to each other and to the
ground. The rods carry the same current in the
same direction. One rod is held in place while
the other floats 8.2 mm beneath it. Determine
the current in the rods.
What direction is the net force on the loop from the wire?
A) Left
B) Right
C) Up
D) Down
E) No net force
Magnetic field of a Solenoid
Magnetic field from a loop
• B = µ0nI in the interior of a long solenoid
n = number of turns per unit length
• Solenoids also referred to as electromagnets
B=
µ0 I
2R
at the centre B = N
0 I
2R
for N turns
Ferromagnetism
Magnetism due to motion of electrons in atoms:
-- orbital motion (not so important)
-- electron spin (most important)
Ferromagnetic materials: magnetic domains with net
alignment of electron spins (e.g. Fe, Ni, Co)
Induced Magnetism: external magnetic field
induces growth and alignment of domains: gives
material an overall magnetic field
Electromagnetic Induction
• A changing magnetic field can produce an electric
current in a coil
• There is an induced emf in the coil which can create
an induced current
One way: relative motion of magnet and coil causing
an increase or decrease of magnetic field at the coil
Two other ways:
Generator: rotation of
coil in a fixed magnetic
field
Transformer: changing
field at the coil due to AC in
a nearby electromagnet
(step-down, step-up)
EMF Induced in a Moving Conductor
Free electrons are forced to
move to one end of the rod
• Separated +ve, -ve charge
creates a motional emf
ℇ = vBL (for v, B, L ⊥)
• Current can flow as long
as rod moves
There is a second magnetic
force on induced current
which opposes the force
moving the rod
ex. Suppose a circuit consists of a 6.0Ω
heater that consumes 15W and a 1.2m
conducting bar that moves at constant speed
along the rails that complete the circuit. The
circuit is in a 2.4T magnetic field. How fast is
the bar moving?
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
A conducting ball is moving through a magnetic field
as shown. Recall that a conductor has lots of electrons
that are free to move around inside it. The ball will ...
A) be polarized
B) be polarized
+
-
X
X
+
C) be polarized - +
B
X
X
v
X
X
X
X
D) be polarized + E) not be affected
A loop of wire is brought near a long straight wire
carrying a current I to the right. The direction of the
current induced in the loop is ...
A) clockwise
I
B) counter-clockwise
v
C) zero
D) not enough info.
Electromagnetic Waves
• Electromagnetic waves are perpendicular (transverse)
electric and magnetic fields travelling through space
• Electromagnetic waves are created by accelerating
electric charges
• Light is an electromagnetic wave, but light is only a
tiny part of the electromagnetic spectrum
Generation of EM Waves
Apply an alternating voltage
applied to antenna wires:
oscillating charges produce
oscillating electric field
Near Field
Oscillating charges
constitute an oscillating
current, which produces an
oscillating magnetic field
Electromagnetic Wave
Changing magnetic field produced by the antenna
produces a changing electric field ...
The changing electric field produces a changing
magnetic field ...
Vibrating electric and magnetic fields regenerate each
other to make a travelling electromagnetic wave
Far Field
Detection of radio waves
Electromagnetic Spectrum
• Frequency and wavelength vary along the EM spectrum
• All waves travel with the same speed (c)
• Energy ∝ frequency (E=hf)
c=
Properties of EM Waves
The Speed of Light: Effects
• Transverse waves – they can be polarized (24.6)
Michelson's rotating mirror
• Do not require a medium for propagation
Laser ranging
• EM waves carry energy
• Speed of propagation in vacuum: c=3.00 x 108 m/s –
both measured and theoretically predicted (Maxwell)
• Speed of propagation in a medium < c – depends on the
frequency and the refractive index of medium
Special Relativity
Cerenkov Radiation
• Doppler shift can be used to determine relative velocity
Doppler Effect
• Doppler shift for EM waves depends on relative velocity
Absorption of EM Waves
• Absorption of energy:
• Temperature change
• Chemical change (worse)
• Damage:
• Mostly due to UV
UVA: 380—320 nm
UVB: 320—280 nm
UVC: 280—200 nm
UV Absorption and Damage
UVA:
aging of skin (wrinkles, sagging)
damage to eyes
UVB:
sunburn
cataracts
UVC:
DNA mutations
skin cancer
EM Wave Receptors in the Eye
• Rods: sensitive to most colours (but not red), and can
detect low levels of light
• Cones: three types, each most sensitive to a given range of
wavelengths (RGB). Less sensitive then rods at low intensity
• How do we identify different colours with only RGB cones?
• Why are our eyes most sensitive to yellow-green light?
Computer Screens and Colours
• Each pixel on a computer screen contains three subpixels, each sub-pixel displaying red, green, or blue
• Each sub-pixel can have a different brightness, and
different colours are produced with additive colour mixing
• With 256 different intensities per sub-pixel can have 16.8
million different colours (256x256x256)