Download Curved Surfaces also reflect light. One example is a Spherical Mirror

Loops of Wire
Every wire with a current
creates a magnetic field.
(Recall: current flows from
the positive to negative
terminals.)
Every part of the wire
creates a B field around it.
The B field induced by a
loop of wire .....
...Resembles the B field of
a Bar Magnet.
Magnetic Field lines leave
the magnet at its N pole
then curve around to the S
pole.
...behave like bar magnets with the opposite poles together.
They attract.
Many loops of current can be placed together.
(Their loops will attract each other)
This is called a solenoid.
It produces a uniform magnetic field inside.
It is the magnetic equivalent of....
a Capacitor!
A solenoid will induce a
magnetic field. So it is also
called an Inductor.
Inductors can also be
included in circuits.
Magnetic Fields in Atoms
In a simple model of the H atom, the electron orbits the proton 6 x 1015
times each second! This amounts to a current, I = 10 -3 A.
Loops of current create B fields. Using Ampere’s law, we can calculate
the magnetic field of ONE ATOM, due to an electron’s orbit.
Batom = 12 Tesla !
That’s more than an MRI magnet...
.... and that’s just 1 atom!
(Electrons also have their own spin which
generates an even stronger B field)
So, why isn’t everything a magnet?!??
Ferromagnetism:
Some materials* have magnetic “domains”
They are normally oriented randomly, so there is no
net magnetic field.
*e.g. Iron, Nickel Cobalt
The domains can be aligned by an external field.
Geology Application: Mid Ocean Ridges
At the Earth’s Mid Ocean Ridges, new rock is created.
As it cools and solidifies, the Earth’s magnetic field re-orients some
of the domains, and is “imprinted” into the new rock.
But... Earth’s magnetic field
sometimes reverses polarity!
This was discovered when
geologists noticed matched
magnetic patterns on either
side of a mid-ocean ridge.
Earth’s B field reverses after a
period of 10,000 to 1 million
years.
Why?
We’re not exactly sure...
Summary: There are two types of Right Hand Rule, for two purposes:
1.) If a charge moves (or a current exists) in a B field, use RHR#1 to
find the force on the charge: Start with your finger(s).
2.) If a wire has a current, use RHR#2 to find the magnetic field that
circulates around the wire. Start with your thumb
Chapter 23
Faraday’s Law of Induction
Optional Reading: Sec. 8,9,10
• RL Circuits
• Energy Stored in a Magnetic Field
• Transformers
We have
discussed
the interaction
between
circuits
and magnetic
We have
discussed
the interaction
between
circuits
and magnetic
fields.fields.
1.)
2.)
1.) Magnetic
deflect
charges
and wires
push wires
with currents.
Magnetic
FieldsFields
deflect
charges
and push
with currents.
2.) Wires
currents
produce
circular
magnetic
Wires
with with
currents
produce
circular
magnetic
fields.fields.
These B fields were static.
But these
magnetic
But these
magnetic
fieldsfields
were were
not changing.
not changing.
What
if wire experiences a mag.
field that changes with time???
happens
if a circuit
WhatWhat
happens
if a circuit
experiences
a magnetic
experiences
a magnetic
field field
Let’s which
find out....
changes?
which changes?
would
B to
field to
WhatWhat
would
causecause
the Bthe
field
change
anyway?
change
anyway?
Figure 23-2B
Figure 23-2A
Figure 23-2C
Induced Currents
A current can be induced by moving the magnet into the loops of wire
(thus increasing B with time)
But the current drops to 0 when the magnet stops.
Even if it is inside the loops!
So the current depends not on B, but the change in B.
The strength of the induced current is proportional to the rate at
which magnetic field is changing.
Terms
Since currents are driven by voltages, we call this an:
induced voltage (or induced “electromotive force” e.m.f)
Vinduced = ε
Unnumbered Figure Page 804
Magnetic Field is increasing. (Lines becoming more dense)
Magnetic Flux
Experiments show that the current induced in the loop of
wire also depends on area of that loop (A), and how it
is oriented.
We can combine these three concepts:
B, magnetic field
A, area of loop of wire
θ, “normal angle” of the loop with respect to B
to define a new quantity, Magnetic Flux (Φ)
Magnetic Flux
Loop with area (A) positioned at angle (θ) with respect to
the Magnetic Field has a Magnetic flux (Φ) of:
It is the change in Magnetic flux
that creates the current in a loop
of wire.
Magnetic Flux (!) is the amount of magnetic field (!) “Flowing”
through an area A. The angle between the loop’s normal (or
perpendicular) direction and B is: !
(" =90)
If the loop is perpendicular to B , then " =0
So the Magnetic Flux: ! = # x A.
Magnetic Flux (!) can be zero if no magnetic field (!) “Flows Through”
through the area in question (A)
If the loop is parallel to B, (" =90) then Magnetic Flux:
! = 0.
Faraday’s Law of Induction
Faraday’s law: When the magnetic flux through a
wire loop changes with time, an EMF (ε) is induced.
VInduced =
ε = Induced Voltage (e.m.f)
ΔΦ = Change in Magnetic Flux
Δt = Change in Time
N = number of loops
The minus sign... will be explained later.
Example
If a single circular loop with radius 2.5 cm is suspended at 30o in a B
field of 0.625 T, what is the magnetic flux through the loop?
Φ = B A cos (θ)
Compute area: A = 3.14 x (0.025 m)2 = 0.0019 m2
Φ = 0.625 T (0.0019 m2) cos (30o)
= 0.001 T m2 (= 0.001 Wb)
What about 90o ?