Download A rectangular wire loop is at rest in a uniform magnetic field B of

Notes: Magnetism: Part 2
Last Info about Magnetism
𝑩=
𝝁𝟎 𝑰
𝟐𝝅𝒓
0  4 x 107
T m
A
 This has to do with how well the surroundings can be magnetized.
Vector Nature of Magnetic Fields
Practice Problem: Point Between Two Wires
Practice Problem: Find the Magnetic Field in the Corner
Find the magnetic field in the lower right hand corner, given the current and distance l.
Magnetic Force Between Two Currents
Practice Problem: Force Between Two Wires
Induction: Producing Electricity from Magnetism
Magnetic Flux
Imagine we had a wire loop hanging out in a B field. Flux, is the magnetic field strength passing through that loop.
⃗ ⃗⃗⃗⃗
Φ=𝐵
∙ 𝐴 = 𝐵𝐴𝑐𝑜𝑠𝜃
Notice in this situation, area is a vector. This isn’t real. We actually generally think of area as having a stick coming out of
it. That is what we consider the “direction” of the area.
The units will be 𝑇 ∙ 𝑚2 or Wb, Webber.
Practice Problem: Calculating Flux
A rectangular wire loop is at rest in a uniform magnetic field B of magnitude 2 T that is directed out of the page. The loop
measures
5 cm by 8 cm, and the plane of the loop is perpendicular to the field, as shown. The total magnetic flux through the loop is
(A) zero (B) 2 x 10-3 T-m2 (C) 8 x 10-3 T-m2 (D) 2 x 10-1 T-m2 (E) 8 x 10-1 T-m
Using Magnetic Flux to Cause Electricity
Faraday’s Law of Induction
𝜀𝑖𝑛𝑑 =
−𝑁∆Φ𝐵
∆𝑡
Where N is the number of loops,
∆Φ
∆𝑡
indicates how much the magnetic field strength will change over time.
Ways of Inducing a Current
Let’s look back at Faraday’s Law of Induction and the equation for flux
𝜀𝑖𝑛𝑑 =
−𝑁∆Φ𝐵
∆𝑡
⃗ ⃗⃗⃗⃗
Φ=𝐵
∙ 𝐴 = 𝐵𝐴𝑐𝑜𝑠𝜃
we see that there are only so many ways we can change the flux.
We can induce a magnetic field by:
1. Altering the Magnetic Field
2. Altering the Area
3. Changing the angle of the loop
Practice Problem: Calculating Emf
A square loop of copper wire is initially placed perpendicular to the lines of a constant magnetic field of 5 x 10 -3 tesla. The area
enclosed by the loop is 0.2 square meter. The loop is then turned through an angle of 90° so that the plane of the loop is parallel to the
field lines. The turn takes 0.1 second. The average emf induced in the loop during the turn is
(A) 1.0 x 10-4 V (B) 2.5 x 10-3 V (C) 0.01 V (D) 100 V (E) 400 V
Lenz’s Law
Basic Idea
The 𝜀𝑖𝑛𝑑𝑢𝑐𝑒𝑑 tries to counteract any change in the flux.
This is an outgrowth of the law of conservation of energy.
Solving these problems:
1. Figure out if there is any flux (changing magnetic field through the loop) No flux 𝜀𝑖𝑛𝑑𝑢𝑐𝑒𝑑 = 0.
2. If there is a magnetic flux, decide whether it is increasing or decreasing.
If magnetic flux is increasing, then the original magnetic field and the induced magnetic field are in OPPOSITE
DIRECTIONS.
If the magnetic flux is decreasing, then the original magnetic field and the induced magnetic field are in the SAME
DIRECTION.
Practice Question: Changing the Field
A single circular loop of wire in the plane of the page is perpendicular to a uniform magnetic field B directed out of the
page, as shown. If the magnitude of the magnetic field is decreasing, then the induced current in the wire is
(A) directed out of the paper
(B) directed into the paper
(C) clockwise around the loop
(D) counterclockwise around the loop
(E) zero (no current is induced)
Practice Question: Moving a Magnet Into a Magnetic Field
Imagine you pushed the magnet into the loop. Which direction would the induced current flow?
What if we switched the magnet around?
A Loop Moving Through Into a Magnetic Field
A common problem involves sending an conducting loop into a constant magnetic field.
As the loop enters the magnetic field, the flux changes, and a current is induced.
Practice Problem: Loop into a Field
In the loop on the left, which direction would you expect the induced current to go?
Never use arrows to describe this, unless you are physically drawing them on the wire. Otherwise, use clockwise or
counterclockwise.
Moveable Wire Bar Problems
Sometimes, they like to do a variation of this. They like to have a loop where one side can be moved back and forth
along rails.
If we were moving the bar according to the picture on the left, which way
would the induced current flow?
If you were pulling on the bar, which direction would you feel a force?
Rod in a Magnetic Field
Let’s say we had a conducting rod and we sent it through a magnetic field. What would happen?
Equation for a rod through a Magnetic Field
𝜖 = 𝐵𝑙𝑣
Practice Question
A 0.20 m long copper rod has constant velocity 0.30 m/s traveling through a uniform magnetic field of 0.060 T. The rod, velocity, and
magnetic field are all mutually perpendicular. What is the potential difference induced across the rod’s length?
A) 0.0036 V B) 0.040 V C) 0.090 V D) 1.0 V E) 25 V