Transcript induced magnetic field - Madison Public Schools

Lenz’s Law and Faraday’s Law
Michael Faraday
Faraday’s Discovery
A changing
magnetic flux
through a loop of
wire causes an
induced current in
the wire.
Any induced current in a loop of wire will also have
an induced magnetic field associated with it.
In order to determine the direction of the induced B
field in the center of the loop, we can use RHR #3!
Right-Hand Rule #3
If you wrap your fingers
around like the current in a
loop of wire, your thumb
will show the direction of
the magnetic field in the
center of the loop caused
by that current!
I
B
Lenz’s Law
The induced B field in a loop of wire will oppose the
change in magnetic flux through the loop.
If you try to increase the flux
through a loop, the induced
field will oppose that increase!
Binduced
If you try to decrease the flux
through a loop, the induced
field will replace that decrease!
Binduced
Flux and Change in Flux
Magnetic flux is a vector that always points in
the same direction as the magnetic field.
However, it is really ΔΦ that we are interested in!
If the flux is increasing, then ΔΦ points
in the same direction as Φ.
If the flux is decreasing, then ΔΦ points
in the opposite direction as Φ.
Φ and ΔΦ Whiteboard
State the direction of the flux and the change in flux through
the loop in each of the following cases.
Φ and ΔΦ
Φ: Into page
ΔΦ: Into page
Φ: Out of page
ΔΦ: Out of page
Φ: Out of page
ΔΦ: Into page
Φ: Out of page
ΔΦ: Zero
Now On To Lenz’s Law!
The induced current will flow so that
its induced magnetic field opposes
the change in flux.
Iinduced
Binduced
Lenz’s Law Challenge Lvl. I
A loop of conducting wire is placed in the region shown
below, in which the magnetic field is increasing in strength.
Which way will the induced current flow in the loop?
Φ: Out of page
ΔΦ: Out of page
Binduced: Into page
Iinduced: Clockwise
Lenz’s Law Challenge Lvl. II
A loop of conducting wire is placed in the region shown below, and
the loop is rotated 90° along the dotted line shown. Which way
will the induced current flow in the loop while it is being rotated?
Φ: Out of page
ΔΦ: Into page
Binduced: Out of page
Iinduced: Counterclockwise
Lenz’s Law Challenge Lvl. III
The two wire loops shown below are moved at constant velocity
near a current-carrying wire. Which direction, if any, will the
induced current flow in each of the wire loops shown below?
Loop 2
Loop 1
v
v
I
Loop 2
Loop 1
v
v
Loop 1
Φ: Out of page
I
Loop 2
Φ: Out of page
ΔΦ: Zero
ΔΦ: Out of page
Binduced: Zero
Binduced: Into page
Iinduced: None
Iinduced: Clockwise
Faraday’s Law
If there is an induced current in a loop of wire, it
must be caused by an induced emf (voltage)!
The induced emf has the same magnitude as
the rate of change of the magnetic flux.
DF
e=
Dt
Getting Quantitative
The loop of wire shown below has a radius of 0.2 m,
and is in a magnetic field that is increasing at a rate
of 0.5 T/s. The wire contains a 3 Ω resistor.
r
a) What is the induced emf?
b) What is the induced current, and which way does it flow?
Solution
Since the area of the loop is constant,
Δ(BA) = AΔB
DF
D(BA)
DB
e=
=
=A
Dt
Dt
Dt
a) ε = 0.06 Volts
b) I = ε/R = 0.02 A clockwise
Quiz Tomorrow
• Lenz’s Law and Faraday’s Law
• Similar to HW problems and whiteboards
• Study it up!!