Download Notes-Induction - IHS Physics Mr. Arnold

Notes: Electromagnetic Induction (25.1-25.4)
Electromagnetic
Induction
•
•
•
•
•
•
•
Magnetic Flux
Faraday found that there is a current in a coil of wire if and only if the
magnetic field passing through the coil is changing.
The current in a circuit due to a changing magnetic field is called an
induced current.
The creation of an electric current by a changing magnetic field is an
example of electromagnetic induction.
A system will respond so as to oppose changes in magnetic flux.
A change in magnetic flux will be partially offset by an induced magnetic
field whenever possible.
Changing the magnetic flux through a wire loop causes current to flow in the
loop.
This is because changing magnetic flux induces an electric potential.
Flux is Latin for “flow.” Let’s look at of magnetic
flux passing through a loop in the same way we
think about the amount of air a fan blows
through a loop.
• The amount of air flowing through a loop
depends on the angle.
• Tipping the loop changes the amount of
air through the loop.
How would you want the loop aligned with the
field for maximum flux?
How would you want the loop aligned with the
field for minimum flux?
How would you want the loop aligned with the field for intermediate flux?
How do we calculate magnetic flux?
What are the units for flux?
Sample Problem
Calculate the magnetic flux through a rectangular wire frame 3.0 m long and 2.0 m
wide if the magnetic field through the frame is 4.2 mT.
a) Assume that the magnetic field is perpendicular to the area vector.
b) Assume that the magnetic field is parallel to the area vector.
c) Assume that the angle between the magnetic field and the area vector is
30°.
Summary
Notes: Electromagnetic Induction (25.1-25.4), cont.
Sample Problem
Assume the angle is 40°, the
magnetic field is 50 mT, and the
flux is 250 mWb. What is the
radius of the loop?
Lenz’s Law
There is an induced current in a closed, conducting loop if and only if the magnetic
flux through the loop is changing. The direction of the induced current is such that
the induced magnetic field opposes the change in the flux.
What three factors can cause an induced current?
To determine the direction of the induced magnetic field:
1. Determine the direction of the applied (existing) magnetic field that passes
through the loop.
2. Determine how the flux is changing. (Is it increasing, decreasing, or staying
the same?)
3. Determine which way the induced magnetic field will point in order to
oppose the change in the flux.
4. Use the RHR to determine the direction of the induced current in the loop.
Sample Problem
The magnetic field is increasing at a rate of 4.0
mT/s. What is the direction of the current in the wire
loop?
The magnetic field is increasing at a rate of 4.0 mT/s.
What is the direction of the current in the wire loop?
The magnetic field is decreasing at a rate of 4.0
mT/s. What is the direction of the current in the wire
loop?
A loop is moved toward a current-carrying wire
as shown. As the wire is moving, is there a
clockwise current around the loop, a
counterclockwise current, or no current?
Explain.
Summary
Notes: Electromagnetic Induction (25.1-25.4), cont.
Faraday’s Law
The induced emf is the rate of change of the magnetic flux through the loop,
regardless of what causes the flux to change:
 
 B
t
Why is there a negative sign?
What if there are multiple loops, like in a solenoid?
Sample Problem
A coil of radius 0.5 m consisting of 1000 loops is placed in a 500 mT magnetic field
such that the flux is maximum. The field then drops to zero in 10 ms. What is the
induced potential in the coil?
Sample Problem
A single coil of radius 0.25 m is in a 100 mT magnetic field such that the flux is
maximum. At time t = 1.0 seconds, field increases at a uniform rate so that at 11
seconds, it has a value of 600 mT. At time t = 11 seconds, the field stops increasing.
What is the induced potential
a) at t = 0.5 seconds?
b) at t = 3.0 seconds?
c) at t = 12 seconds?
Summary
Notes: Electromagnetic Induction (25.1-25.4), cont.
Motional emf
Motional emf is the voltage produced by the
motion of a conductor in a magnetic field.
What would happen to the ions in this conductor
as it moves to the right in this magnetic field?
Derive an equation for the potential difference between the two ends of the
conductor:
Motional emf in a circuit
Sample Problem
A moving conductor could have an emf, but it could not sustain a current because
the charges had nowhere to go. If we include the moving conductor in a circuit, we
can sustain a current. One way to create the circuit is to add a fixed U-shaped
conducting rail along which the wire slides.
a. How much current flows
through the resistor?
b. How much power is dissipated by the resistor?
c.
In which direction is the induced current through the resistor (up or down)?
d. Assume the rod is being pulled so that it is traveling at a constant 2 m/s.
How much force must be applied to keep it moving at this constant speed?
e. How much power is needed to keep it moving at this speed?
How is this possible, in terms of Faraday’s law?!?
Summary