Download D. Magnetic Fields

NOTES
Unit 12: Electricity and Magnetism – Magnetism
OBJECTIVES:1
III. Electricity and Magnetism
D. Magnetic Fields
1. Forces on moving charges in magnetic fields: Students should understand the force
experienced by a charged particle in a magnetic field so they can:
a. Calculate the magnitude and direction of the force in terms of q, v, and B, and explain
why the magnetic force can perform no work.
b. Deduce the direction of a magnetic field from information about the forces experienced
by charged particles moving through that field.
c. Describe the paths of charged particles moving in uniform magnetic fields.
d. Derive and apply the formula for the radius of the circular path of a charge that moves
perpendicular to a uniform magnetic field.
e. Describe under what conditions particles will move with constant velocity through
crossed electric and magnetic fields.
2. Forces on current-carrying wires in magnetic fields: Students should understand the force
exerted on a current-carrying wire in a magnetic field, so they can:
a. Calculate the magnitude and direction of the force on a straight segment of currentcarrying wire in a uniform magnetic field.
b. Indicate the direction of magnetic forces on a current-carrying loop of wire in a magnetic
field, and determine how the loop will tend to rotate as a consequence of these forces.
3. Fields of long current-carrying wires: Students should understand the magnetic field produced
by a long straight current-carrying wire so they can:
a. Calculate the magnitude and direction of the field at a point in the vicinity of such a wire.
b. Use superposition to determine the magnetic field produced by two long wires.
c. Calculate the force of attraction or repulsion between two long current-carrying wires.
E. Electromagnetism
1. Electromagnetic induction (including Faraday’s law and Lenz’s law)
a. Students should understand the concept of magnetic flux so they can:
1.) Calculate the flux of a uniform magnetic field through a loop of arbitrary orientation.
b. Students should understand Faraday’s law and Lenz’s law so they can:
1.) Recognize situations in which changing flux through a loop will cause an induced emf
or current in the loop.
2.) Calculate the magnitude and direction of the induced emf and current in a loop of
wire or a conducting bar under the following conditions:
a.) The magnitude of a related quantity such as magnetic field or area of the loop is
changing at a constant rate.
1
These are the outlined objectives of the AP Physics B course as laid out by the College Board. We will continue to
build this outline throughout the year. We do not do all of the objectives listed in the AP outline, as some are only
for AP Physics C. Therefore missing numbers or letters is intentional.
NOTES
NOTES:
I. Magnetism Basics
A. Magnets have two ______________________________ (__________________.)

Opposite poles attract; like poles repel.
B. _____________________________________________________ around themselves. Therefore
electrons moving around nuclei create tiny ____________________________ around themselves.
C. __________________________
1. In most materials, the magnetic fields around electrons don’t align and mutually cancel.
2. In ________________________ materials, the ______________________________________
in small regions called ______________________________ about 0.01-0.1mm wide. Each
domain acts as a tiny magnet.
3. When a ferromagnetic material is exposed to an ___________________________, the
_____________________________, and the material becomes magnetized.
o
Sketch…
o
Some magnets only hold the alignment while the field is present.
o
Some magnets hold the alignment when the field is removed and are
__________________________________.
o
Jostling can knock domains back out of alignment.
NOTES
II. Magnetic Force on Moving Charges and Current-Carrying Wires
A. Magnetic fields: Similar to electric fields; point ___________________________________;2
Sketch:
B. _______________________________: Because moving charges generate magnetic fields, when a
____________________________ in an _______________________________, it experiences
magnetic a force ___________________3 to the magnetic field provided that…
1. the ________________________________, and
2. its velocity has a _____________________________________ to the ______________.
3. Because the force is perpendicular to the particle’s movement, magnetic force does
____________________________ on a charged particle.
C. Details:
1. Formula:
so that
where…
o
_____ is the magnetic field
o
_____ is the magnitude of the magnetic force on a test charge
o
_____ is the magnitude of the test charge
o
_____ is the magnitude of the test charge’s velocity
o
_____ is the angle between the test charge’s velocity and the magnetic field4
2. SI Unit: _________ = _________
2
This is the same direction a compass’ north pole would point in the field. Therefore which magnetic pole is near
Earth’s geographical North Pole? ________________ 
3
This is an experimental fact.
4
Therefore force is greatest when velocity is perpendicular to the field and disappears as the velocity becomes
parallel to the field.
NOTES
3. Direction: “________________________________”
**where 𝑣 is the direction a ______________ charge moves.
4. _________ of charged particles in magnetic fields will be ___________________________
_____________________. Figure 21.20 (page 652) is a nice image. There’s also this high-tech
art:5
a. Magnetic force, therefore, acts as a ____________________________, and the
__________of the curved path can be found by:
so
b. Bringing back the idea that magnetic force does no work on a charged particle:
Centripetal force does no work in the same way that magnetic force does no work.
5
By convention, a dot indicates a field or force running out of the plane of the page. An x indicates a field or force
directed out of the page.
NOTES
D. Examples:
1. Example 1: Magnetic force on a single charged particle: A proton in a particle accelerator has
a speed of 5E6 m/s. The proton encounters a magnetic field whose magnitude is 0.40 T and
whose direction makes an angle of 30⁰ with respect to the proton’s velocity. The mass of a
proton and of an electron are on your formula sheets. Find (a) the magnitude and direction of
the magnetic force on the proton and (b) the acceleration of the proton. (c) What would be the
force and acceleration if the particle were an electron instead of a proton?
2. Example 2: Two charged particles of equal charge move in a magnetic field. Particle 1 is
moving perpendicular to the field. Particle 2 is moving at an angle but with a perpendicular
component equal to the velocity of particle 1. Which experiences the greater force?
NOTES
3. Example 3: An electron travels at 2.0E7 m/s in a plane perpendicular to a 0.010 T magnetic
field. Describe its path.
4. Example 4: It is common for charged particles to travel in spirals in magnetic fields. How can
this happen? This is how the aurora borealis occurs from ions enter the atmosphere near the
poles where the magnetic force is the strongest. The accelerating ions become energetic, causing
electrons to emit light.
5. Example 5: How could you make a charged particle move with a constant velocity in a
magnetic field? (Being able to answer this is a learning objective.)
NOTES
E. Magnetic force _____ current-carrying wire
1. Because moving charges generate magnetic fields, when a current-carrying wire is placed in
an external magnetic field, it __________________ and therefore experiences magnetic force.
2. Formula for magnetic force on a current-carrying wire:
𝑡
Multiply the whole thing by 𝑡 to get
where _____ equals __________ (𝐼) and _____ equals displacement (_______________, ℓ)
to get
3. The direction of the force follows the ______________________.
4. Example 6: A current travels to the right in a wire running horizontally in a uniform magnetic
field of strength 1.42 T that points out of the page. The wire has a length of 10.0 cm, and the
current in the wire is 0.245 A. What is the magnitude and direction of the magnetic force?
NOTES
5. Current-carrying loops rotate in magnetic fields due to different directional forces on each
side of the loop.

Example 7: In the image below, the current runs upward on the left portion of the loop and
downward on the right portion of the loop. Which way does the loop rotate?
III. Magnetic Fields Created _____ Current-Carrying Wires
A. Since moving charges create magnetic fields, current-carrying wires create magnetic fields
_______________ themselves.
1. Fields created by wires form _________with the wire at the center. The magnetic field
___________________________ to the circle and follow the right-hand rule as follows.
X
Current into page:
Current coming out of page:
Magnetic field is clockwise.
Magnetic field is counterclockwise.
NOTES
2. Magnetic force created by a long, straight wire:
o
Formula:
where…

_____ is the strength of the magnetic field at…

_____ is the radial distance from the wire

_____ is the permeability of free space where 𝜇0 = 4𝜋 x 10-7 T∙m/A

_____ is the current
B. __________________________: Two (or more) current-carrying wires create a combined effect
on the region.
1. Example 8: Use superposition to determine the magnetic field produced by two long wires. The
two wires of a 2.0m long appliance cord are 3.0mm apart and carry a current of 8.0 A. Calculate
the force between these wires. (Assume the current is dc and that the current flows in opposite
directions.)
2. Direction of the force:
a.) _____________ currents ____________, because at the center, B1 points __________ B2.
b.) _____________________ currents _____________, because at the center both magnetic
fields point in the __________________________and therefore repel.
NOTES
IV. ________________________________
A. _______________________ refers conceptually to the ____________________________
passing through a region.6
1. Conceptually: A stronger magnetic flux means the magnetic field is stronger in a region.
2. Magnetic flux is _____________ to the __________________________ 7 of the magnetic
field lines passing through an ___________.
3. Formula:
where
a. _____ is the magnetic flux measured in _____________ (_____________)
b. _____ is the angle between the direction of the magnetic flux and the _____________l to
the area of the region: (Pay attention to this. It can be a source of confusion.)
B. _______________________________________: Induced _____ and induced current
1. When a wire with no current sits at rest in a magnetic field, nothing happens. However,
we’ve seen that when we run current through a wire in a magnetic field, the wire can move
(down in the example, left.) Likewise, if we move a magnet near a wire with no current, we
can induce current in the wire. (Move the wire up (or the magnet down) in the example to
the right, a magnetic force would cause current to flow into the page.)
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7
All force fields have a flux: Electric flux, gravitational flux
Think of it like sunshine through a window. The angle of the rays matters.
NOTES
2. __________________________: The “force” that moves electrons in a wire due to a
_______________________________________between the wire and an external magnetic
field such that
where…
o
_____ is the electromotiveforce
o
_____ is the velocity of the relative motion
o
_____ is the magnetic field
o
_____ is the length of the conductive material (e.g., rod or wire)
3. __________________________: Current that results from the creation of an induced emf.
(Important: Relative motion must be occurring, or the emf reduces to zero again, halting
current.)
4. __________________________: The process of creating an induced emf.
NOTES
C. __________________________: When we create a _____________and create relative motion
by _____________ the loop in a _______________________ 8, the ______________________as
____________ changes. This creates an emf according to the formula:
so that the __________________________and how little __________________________ to
___________________________ (faster loop rotation) creates ________________.

Example 9: A 0.1m x 0.1m loop is rotated so that it makes a full turn every 0.04s in a
magnetic field of 2T. What is the emf produced? (Hint: To go from phi equals 0⁰ to phi
equals 90⁰ takes ¼ of the time.)
D. ________________________
1. Lenz’s law explains the __________________________and explains the negative sign in
Faraday’s Law.
2. The direction of the induced current will be to _____________________________________
__________________________. Conducting loops __________________________to
magnetic flux inside of them by ________________________to _____________ the change.

Analogy: Mass resists changes in velocity as conducting loops resist changes in the flux
inside of their loops.

Counteranalogy-type thing: If the loop DIDN’T do this and instead created current that
enhanced the field emf would grow as B grew on and on infinitely. This is impossible by
the conservation of energy.
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OR by rotating a magnet around a stationary loop of wire
NOTES
3. Example:
a. Which way will current flow in a loop if a magnetic field is flowing into the page and
is increasing in strength? (first picture)
b. Which way will current flow in a loop if a magnetic field is flowing out of the page
and is increasing in strength? (second picture)
c. Which way will current flow in a loop if a magnetic field is flowing into the page and
is decreasing in strength? (third picture)
d. Which way will current flow in a loop if a magnetic field is flowing out of the page
and is decreasing in strength? (fourth picture)
Increasing
Increasing
Decreasing
Decreasing