Download Magnetic Fields and Magnetic Forces NOTES

Magnetic Fields and Magnetic Forces
Properties of magnets:
1. A magnet has polarity - it has a north and a south pole; you cannot isolate the
north or the south pole (there is no magnetic monopole)
2. Like poles repel; unlike poles attract
3. A compass is a suspended magnet (its north pole is attracted to a magnetic south
pole); the earth’s magnetic south pole is within 200 miles of the earth’s
geographic north pole (that is why a compass points "north")
4. Some metals can be turned in to temporary magnets by bringing them close to a
magnet; magnetism is induced by aligning areas called domains within a magnetic
field
5. Permanent magnets are formed of metallic alloys or metals such as iron, nickel, or
cobalt.
Every spinning electron is a tiny magnet. Electrons spin about their axis like a top spins
around its axis. Thus, the electron is a moving charge. Moving charges create a magnetic
field. A pair of electrons spinning in the same direction create a stronger magnetic field; a
pair of electrons spinning in opposite directions create a weaker magnetic field. The
magnetic fields produced by spinning electrons in ferromagnetic materials do not all
cancel each other out.
Magnetic field (symbol is B and SI unit is the Tesla or T)
the environment around a magnet in which the magnetic forces act. Another
common unit for magnetic field strength is the gauss (G); 1 G = 1 x 10-4
Magnetic field lines
they represent the area around a magnet; magnetic field lines outside of the
magnet flow from the north to the south pole
Domain
Atoms of ferromagnetic materials act in groups called domains; atomic magnets
in each domain are aligned so that each domain is a microscopic bar magnet; the
domains align themselves with an external magnetic field. Each domain behaves
like a tiny magnet and has a north and a south pole. In unmagnetized materials,
the domains are randomly arranged. In magnetized materials, the domains are
aligned. Anything that randomizes the alignment of the domains destroys the
magnetic properties of a material (dropping a magnet or heating it)
Comparing electricity and magnetism:
Electricity
Magnetism
+ and - charges
N and S poles
like charges repel
like poles repel
unlike charges attract
unlike poles attract
electric monopole exists
no magnetic monopole
electric field lines flow from + to - magnetic field lines flow from N to S
density of lines equals strength of
E
density of lines equals strength of B
SI unit: ampere, 1 A = 1 C/sec
SI unit: Tesla, 1 T = 1 N/Amp meter
E exerts force on a charge, or E =
F/q
Field exerts force on a moving charge, or B =
F/(qvsin)
Curie temperature Important constants to know for this section: The charge of an
electron (or proton) is 1.6 x 10-19C and one Volt is equivalent to 1.6 x 10-19 J of energy.
Curie temperature temperature above which a material loses all magnetic properties
Oersted (1820) found that an electric current in a wire produces a magnetic field around
it; a stationary charge does not create a magnetic field
Right-hand rules predict the direction of magnetic fields produced by a current. They are
used for conventional current flow. Use your left hand to predict the direction an electron
or negative charge would follow.
RHR #1 - Straight Wire Conductor
Curl the fingers of the right hand into the shape of a circle. Point the thumb in the
direction of the current and the tips of the fingers will point in the direction of the
magnetic field.
RHR #2 - Solenoid
Curl the fingers of the right hand in the direction of the current. Your thumb is the
north pole of the electromagnet.
RHR #3 - Magnetic Force
Extend the right hand so that the fingers point in the direction of the magnetic
field and the thumb points in the direction of the current. The palm of the hand
then pushes in the direction of the magnetic force.
Forces Due to Magnetic Fields
Ampere found that a force is exerted on a current-carrying wire in a magnetic
field
F = B I L sin 
where B is the magnetic field in Teslas (T), I is the curent, L is the length of wire
in meters, and  is the angle. Only the perpendicular component of B exerts a
force on the wire. If the direction of the current is perpendicular to the field
(=90), then the force is given by
F=BIL
We know how to measure force, current, and length. Thus B can be calculated by
using
The force produced by a magnetic field on a single charge depends upon the
speed of the charge, the strength of the field, and the magnitude of the charge.
F = q v B sin 
where q is the charge in Coulombs and v is the velocity of the charge. If =90,
then F = q v B
How speed affects the force on a charged particle moving in a magnetic field.
Effects of speed of particle in a Magnetic Field
http://www.sciencejoywagon.com/physicszone/lesson/08magnet/partmagn/index.
htm
If the charged particle moves parallel to the field lines (=0), then the magnetic
force on the particle is zero. If a charged particle is moving perpendicular to a
uniform magnetic field, the path of the charged particle is an arc (or circle). The
magnetic force is the source of the centripetal force on the charged particle. This
relationship can be used to find the radius of the arc.
(m v2)/ r = q v B
Since the magnetic force is perpendicular to the velocity of the charged particle,
the force does not cause the speed of the particle to change, only its direction.
Thus, no work is done by the magnetic force on the charged particle.
Deflection of electron in a Magnetic Field due to Magnetic Force
http://www.sciencejoywagon.com/physicszone/lesson/08magnet/deflecte/default.
htm
The magnetic field near a long straight wire is directly proportional to the current
I in the wire and inversely proportional to the distance r from the wire. The
magnetic field at any point a distance R away from a straight-wire conductor can
be calculated using,
or, it can be written in its true form (This is an important formula for the AP B
exam.)
where o is a constant called the permeability of free space and has a value of 4
x 10-7 T m/A
Since a wire carrying a current produces a magnetic field and the wire
experiences a force when placed in a magnetic field, two current-carrying wires
exert a force on each other. The force exerted on the second wire is only due to
the magnetic field exerted by the first wire. Parallel currents in the same
directions attract each other and parallel currents in opposite directions repel each
other.
Force on a Loop of Wire (represented by multiple choice questions on the AP
B exam in which you predict the direction of current, etc.)At the center of the
loop, the magnetic field is perpendicular to the plane of the loop. If there are N
loops, the strength of the magnetic field at the center of the loop is given by
multiplying the following by N. The direction of the magnetic field at the center
of the loop can be determined using a RHR (the thumb is pointed in the direction
of the current and the curled fingers are placed at the center of the loop, then the
palm pushes in the direction of the magnetic field.)
Electromagnetic Induction
There are two ways that electricity and magnetism are related: an electric current
produces a magnetic field and a magnetic field exerts a force on an electric
current or moving charged particle. Henry and Faraday independently found
found that a current could be induced in a wire by moving it in a magnetic field.
An electric current is generated in a wire when the wire cuts across magnetic field
lines.
Faraday found that a steady magnetic field does not produce any current, only a
changing magnetic field produces an electric current.
Hints for the AP B exam:
1. Approximately, two out of every three years one of the free response
questions involves a situation where a charge is accelerated through two
charged plates. The charge then enters a magnetic field whose direction
causes the charge to move in a circle. These are common questions that
are asked:
o Calculate the speed of the charge as it exits the region between the
two charged plates.
o Draw the direction of the electric field between the two charged
plates.
o If there is also a magnetic field between the two charged plates in
addition to the electric field, explain the relationship between the
two fields that allows the charge to pass through undeflected.
o Calculate the radius of the path of the charge in the magnetic field.
2. Remember these three formulas for regions where both electric and
magnetic fields exist: V=Ed, qE=F, and F=qvB. Manipulating these
formulas allows you to express the velocity of the charge in terms of E and
B. Manipulating these formulas allow you to write an expression for the
accelerating voltage in terms of v, B, and d.
3. Remember, if the charge is moving in a circle, the magnetic force provides
the centripetal force. This allows you to calculate the radius.
4. Remember, if the charge is moving in a circle and the magnetic field is
perpendicular to it, it does no work on the charge. It only changes its
direction.
5. Sometimes they ask you to calculate the thermal energy dissipated by the
accelerated charge if it is allowed to strike a target. You know its speed;
calculate its energy.
6. A mass spectrometer is also representative of this type of problem. In a
mass spectrometer, the radius of the path of a particle is proportional to its
mass. If you have several particles, you can set up a proportion between
their masses and radii to determine the mass of an unknown particle.
7. If the charged particle moves in a circular path, the centripetal force equals
the magnetic force. This equality can be solved for the ratio of charge to
mass of the particle (q/m).
8. More points are awarded when they ask for a direction if you express it in
terms of positive or negative x, y, or z.
Electromagnetic induction
process of generating a current by using a magnetic field. This is sometimes
called motional emf.
emf = B L v sin 
where emf is the potential difference measured in volts, v is the velocity with
which the wire is moved through the magnetic field B,  is the angle at which the
wire is moved in the magnetic field, and L is the length of the wire
electromotive force (emf)
a potential difference, measured in volts, that can cause an induced current to flow
in a wire. It is not a force, but is a historical term coined before electricity was
understood.
An induced emf is produced by a changing magnetic field.
Electromagnetic Induction
the process where current is produced when either a wire or a magnetic field
move relative to one another; as long as the wire cuts across magnetic field lines
during the motion, a current is produced. A current is induced in a coil of wire if it
is moved into or out of a magnetic field; a current is induced in a coil of wire if a
magnet is inserted or removed from the coil of wire. It doesn't matter if the
magnet or the coil moves-motion or change is required to induce an emf.
Lenz's Law
The direction of the induced current is such that the magnetic field resulting from
the induced current opposes the change in the flow (or flux) that causes the
induced current. It is the change in the flow or flux that causes the induced
current, not the flux itself.
How I predict the direction of the induced current using Lenz's Law:
1. Determine whether the magnetic field strength is increasing or decreasing.
2. Determine the direction in which the original field enters the coil.
3. Determine the direction of the induced magnetic field so that it opposes
the change in the magnetic flux.
4. Use RHR to predict the direction of the current knowing the direction of
the induced magnetic field.
AP B Multiple Choice Questions Hints:There are always questions asked in
which you much predict the direction of an induced current (or emf, )
1. Know the situations when a current or emf is induced in a coil or wire
(Look under the explanation for Faraday's law). Remember - there must be
relative motion or something that causes a changing flux!
2. Be able to write an expression (or calculate) for induced current or emf. In
other words, this can be easily done using a combination of  = Blv sin 
and  = iR.
3. KNOW your RHR that enables you to predict the current through a single
loop or coil. Remember, your thumb points in the direction of the current,
clockwise or counterclockwise. Your fingers enter the loop or coil in the
direction of the magnetic field.
4. Be able to interpret directions in terms of the x, y, and z axes.
5. Be able to calculate (or write an expression) induced voltage using
Faraday's Law. Faraday's law can also be used to calculate the rate of
change of the magnetic field in a moving coil (in other words, it can
calcualte B/t).
6. The faster something is moved, the greater the induced voltage (current)
because emf is directly proportional to the velocity.
Self-inductance
induced emf produced in a coil by a changing current
Mutual inductance
a changing current in one coil induces an emf in another coil
Transformer
an electrical device that increases or decreases AC voltage; a step-up transformer
has more turns in the secondary than in the primary; a step-down transformer has
more turns in the primary than in the secondary. We will call the primary the
incoming voltage or current and the secondary the outgoing voltage or current.
where N is number of turns, V is the voltage, and I is the current. s and p stand for
secondary and primary, respectively.
Magnetic flux (B and SI unit is the Weber, Wb)the number of magnetic field
lines that pass through a surface of area A. A changing magnetic flux produces an
electric field. This is true not only of wires and conductors, but also applies to any
region in space.
B = Bperpendicular A
where Bperpendicular is the component of B perpendicular to the face of the coil
Faraday's Law of Induction Faraday found that the amount of emf induced in a
coil of wire depended upon how rapidly the magnetic field changes in the coil of
wire. The faster the magnetic field changes, the greater the induced emf. If the
flux through a coil of N loops of wire chagnes by an amount B during a time t.
 = - N (B/t)
The negative sign indicates the direction in which the induced emf acts. For our
purposes, we will use Faraday's law to calculate the magnitude of the induced emf
and apply right hand rules for Lenz's Law to determine the direction of the
induced emf.
An emf can be induced three ways:
1. By a changing magnetic field
2. By changing the area of the loop in the field
3. By changing the loop's orientation with respect to the field
Electric Motors and Generators
Electric motor
uses electrical energy to produce mechanical energy. In a motor, there must be a
source of a magnetic field; brushes serve as a connection to the split-ring
commutator, allowing current flow from the motor to an outside source. In order
to continue rotating, current direction must be reversed. This is achieved by the
use of the split-ring commutator and the brushes. The force on a current-carrying
wire in a magnetic field causes an electric motor to rotate
The Electric Motor
Electric generator
uses mechanical energy to create electrical energy; rotation of wire loop in a
magnetic field causes current to be induced. This current changes direction every
180 degrees, producing alternating current (AC current).
The Electric Generator
Magnetic Moment When an electric current flows in a closed loop of wire placed
in a magnetic field, the magnetic force on the current can cause a torque. This is
the basic principle behind meters and motors. If the coil consists of N loops of
wire carrying current I with area A, the torque is given by
 = NIAB sin 
where NIA is the vector quantity called the magnetic dipole moment of the coil.
Its direction is perpendicular to the plane of the coil.
Magnetic Fields, Magnetic Forces, and Electromagnetic Induction Sample
Problems
1. A wire 1 m long carries a current of 5 A. The wire is at right angles to a uniform
magnetic field. The force on the wire is 0.2 N. What is the magnetic field
strength?
2. Now in number one, the wire is directed at an angle of 30. What is the magnetic
field strength?
3. A 10 cm long wire is at right angles to a uniform magnetic field of 0.06 T. A 4 A
current is in the wire. What magnetic force does it experience? What is the
magnetic force if the wire was at an angle of 40 to the magnetic field?
4. A beam of electrons travels at 3,000,000 m/s through a 0.04 T field. What force
does the beam experience?
5. A square coil with 100 loops and sides of 5 cm is positioned perpendicularly to a
uniform 0.06 T magnetic field. It is quickly and uniformly pulled out of the
magnetic field (moving perpendicular to the field) to a region where the magnetic
field suddenly drops to zero. It takes 0.10 sec for the whole coil to reach the fieldfree region. Find the change in magnetic flux in the coil. Calculate the emf and
current induced if its resistance is 100 ohms.
6. A 9.2 cm diameter loop of wire containing 10 turns is initially oriented
perpendicular to a 1.5 T magnetic field. It is rotated so that its plane is parallel to
the field in 0.20 sec. Find the change in magnetic flux in the coil. Calculate the
emf and current induced if its resistance is 50 ohms.
7. A wire 2 m long moves perpendicularly through a 0.08 T field at a speed of 7 m/s.
What emf is induced? Knowing Ohm’s law and that the wire has a resistance of
0.50 ohms, what current flows?
8. The direction of a 0.045 T field is 60 above the horizontal. A wire 2.5 m long
moves horizontally through this field at 2.4 m/s. What is the vertical component
of the magnetic field? What emf is induced in the wire?
9. An electron (mass = 9.11 x 10-31kg) travels at 2 x 107m/s in a circular path in a
0.010 T magnetic field. What is the radius of its path? What is its kinetic energy?
Ans: 0.011 m; 1.82 x 10-16J
10. A transformer has input voltage and current of 12 V and 3 A. It has an output
current of 0.75 A. If there are 1200 turns on the secondary, how many turns are on
the primary? What is the output voltage? Is this a step-up or step-down
transformer?
11. A model electric train requires a low voltage to operate. If the primary coil of its
transformer has 400 turns and the secondary has 20 turns, how many volts will
power the train when connected to a 120 V house circuit? Is this a step-up or stepdown transformer? What is the input current if the current in the train is 0.50 A?
Magnetic Fields and Forces and Electromagentic Induction Homework
1. A wire 0.10 m long carrying a current of 2 A is at right angles to a magnetic field.
The force on the wire is 0.04 N. What is the strength of the magnetic field? What
would its strength be if the wire is at an angle of 35 to the field? Ans: 0.20 T;
0.35 T
2. A wire 0.50 m long carrying a current of 8 A is at an angle of 15 to a 0.40 T
field. What is the magnetic force exerted on the wire? Ans: 0.41 N
3. A beam of electrons moves at right angles to a 0.60 T field. The electrons have a
velocity of 2.5 x 107 m/s. What force acts on the electrons? What force acts if the
beam of electrons move at an angle of 45 to the field? Ans: 2.4 x 10-12 N; 1.7 x
10-12 N
4. A proton moves at right angles to a 0.003 T field directed out of the page. The
proton moves from right to left with a speed of 5 x 106 m/s. What is the
magnitude and the direction of the force the proton experiences? Ans: 2.4 x 10-15
N, towards the top of the page
5. A wire 0.5 m long cuts through a 0.4 T field at a speed of 20 m/s. What is the
induced emf? If the wire is part of a circuit with a total resistance of 6 , what is
the current in the circuit? Ans: 4 V; 0.67 A
6. A wire 20 m long is mounted on an airplane flying at an angle of 60 to the earth's
magnetic field. It flies with a speed of 120 m/s. If the induced emf is 0.12 V, what
is the strength of the earth's magnetic field at this point? Ans: 5.77 x 10 -5 T
7. A step-up transformer has 200 turns on its primary and 3000 turns on its
secondary. If the primary voltage is 90 V, what is the secondary voltage? If the
primary current is 10 A, what is the secondary current? Ans: 1350 V; 0.67 A
8. A copper bar 30 cm long is perpendicular to a 0.8 T field and moves at right
angles to the field with a speed of 0.5 m/s. Determine the emf induced in the bar.
Ans: 0.12 V
9. An emf is induced in a metal rod 0.5 m long that is part of a circuit as it moves
perpendicularly through a 0.15 T field at 2 m/s. The resistance of the rod and the
circuit is 3 . What is the magnitude of the induced emf? What is the current
induced in the rod and the circuit? How large a force is needed to move the rod at
a speed of 2 m/s? Ans: 0.15 V; 0.050 A; 3.75 x 10-3 N
10. A step-up transformer is used on a 120 V line to furnish 1800 V. The primary has
100 turns. How many turns are on the secondary? Ans: 1500 turns
11. A step-down transformer operates on a 2,500 V line and supplies a load with 80
A. The ratio of the primary turns to the secondary turns is 20:1. Determine the
secondary voltage and the primary current. Ans: 125 V; 4 A
12. A 16 cm diameter coil of wire with 50 loops is in a 1.10 T magnetic field. It is
removed fromt the field in 0.15 sec. Calculate the change in flux in the coil. If the
coil has a resistance of 30 , calculate the magnitude of the induced emf and
current. Ans: 0.022 Wb, 7.37 V, 0.25 A
13. The magnetic flux through a coil of wire containing two loops changes from -30
Wb to +38 Wb in 0.42 sec. Calculate the strength of the magnetic field if the coil
has a diameter of 50 cm. Calculate the induced emf. Ans: 346 T, 324 V
A proton moves in a circular path perpendicular to a 1.15 T magnetic field. The radius of
its path is 8.40 mm. Calculate the speed of the proton. Calculate its kinetic energy. The
mass of a proton is 1.67 x 10-27. Ans: 9.26 x 105 m/s, 7.15 x 10-16J AP Magnetostatics
Hand Rule Sample Problems
1. What is the magnitude and direction of the electric field such that q is undeflected
by the magnetic field shown below? What is the speed v of the electron?
2. What is the direction of the magnetic field at point P due to the current in the wire
shown below? If a 5 A current flows through the wire and point P is 4 cm from
the wire, what is the strength of the magnetic field at P?
3. Locate the distance "r" such that the net magnetic field at that point is zero. The
wire on the left carries an upward current of i; the wire on the right carries an
upward current of 2 i. The two wires are separated by distance d.
4. Which path represents the path of a postive particle in the magnectic field, A, B,
or C? Which path represents the path of a negative particle in the magnectic field,
A, B, or C? Which path represents the path of a neutral particle in the magnectic
field, A, B, or C? Which path shows no loss in kinetic energy?
5. A 2 x 10-4 T magnetic field exists between two parallel plates which are 10 cm
long. An electron moving at 3 x 106 m/s enters this region. Draw the electron's
path. Calculate the magnitude of the magnetic force and draw its direction.
Calculate the magnitude of the acceleration caused by the magnetic force. How
long is the electron in the field? What is its vertical displacement while in the
field?
6. A charge eneters a 4 x 10-4 T magnetic field that exists in the region between two
parallel plates and in the region to the right of the two parallel plates as shown
below. It enters the field moving at a speed of 6.9 x 105 m/s. Based upon its path,
what kind of charge is q, positive or negative? What is the radius of its path in the
region to the right of parallel plates? Draw the direction of the electric field
between the two parallel plates that would allow the charge to pass through this
region undeflected. What is the magnitude of the electric field between the two
parallel plates?
7. Find the direction of the magnetic force on the positively charged particle moving
in the various situations shown below through the magnetic field. The red arrow
always indicates the velocity vector of the charged particle. Black always
indicates the direction of the magnetic field.
8. A 20 cm length of wire is free to move between two wires as shown below. All of
the wires are in a magnetic field. The wire segment carries a current of 5 A and
has a mass of 0.20 kg. Assume the wire segment slides without friction. Find the
magnitude and direction of the magnetic field needed to move the wire.
AP Magnetostatics Sample Problems
1. A proton falls from rest through a 334,000 V potential difference. It then enters a
region perpendicular to a 0.5 T magnetic field. With what velocity does it exit the
potential difference? How large is the radius of the circle in which the proton
travels in a counterclockwise direction in the plane of the paper? What is the
direction of the magnetic force? Ans: 8.0 x 106 m/s; 0.167 m; into the paper
2. An electric power line carries a current of 1400 A in a location where the earth’s
magnetic field is 5 x 10-5 T. The line makes an angle of 75 with respect to the
field. Determine the magnetic force on a 120 m length of wire. Ans: 8.11 N
3. A proton enters 1.5 T field with a velocity of 2 x 107 m/s at an angle of 30 with
the field. What is the force on the proton? Ans: 2.4 x 10-12 N
4. A proton moving at 5 x 106 m/s enters a 0.4 T field directed at 30. What is the
magnitude and direction of the proton’s acceleration? What would its magnitude
and direction be if it were an electron? Ans: 9.59 x 1013 m/s2, up; 1.76 x 1017 m/s2,
up
5. An electron in a vacuum is first accelerated by a voltage of 11,000 V and then
enters a region in which there is a uniform magnetic field of 0.1 T at right angles
to the direction of the electron’s motion. What is the electron’s speed when it
enters the field? What is the force on the electron due to the magnetic field? Ans:
6.22 x 107 m/s; 9.95 x 10-13 N
6. A proton in a cyclotron is moving with a speed of 2 x 107 m/s in a circle of radius
0.5 m. What force is exerted on the proton by the cyclotron? What is the
magnitude of the magnetic field necessary to keep it moving in this circle? Ans:
1.34 x 10-12 N; 0.42 T
AP Electromagnetic Induction Sample Problems
1. Consider the arrangement shown below. Assume that R=6  and l = 1.2 m. There
is a uniform 2.5 T magnetic field directed into the page. A 0.5 A current is
produced in the resistor. What voltage is induced in the bar? At what speed should
the bar be moved to produce a current of 0.5 A in the resistor? At what rate is
work done to keep the bar moving at this speed? Ans: 3 V; 1.0 m/s; 1.5 W
2. Two long straight wires are separated by 0.120 m. The wires carry currents of 8 A
in opposite directions; the current in the wire on the left is down and that in the
wire on the right is up. Find the magnitude and direction of the net magnetic fields
at points A, B, and C as shown. Ans: 4.3 x 10-5 T, out, at A; 5.3 x 10-5 T, in, at B;
6 x 10-5 T, in, at C
3. A square, single-turned coil 0.20 m on a side is placed with its plane
perpendicular to a constant magnetic field. An emf of 18 mV is induced when he
area of the coil decreases at a rate of 0.10 m2/s. What is the magnitude of the
magnetic field? Ans: 0.18 T
4. The sliding bar in the figure below has a length of 0.50 m and moves at 2 m/s in a
magnetic field of 0.25 T. Find the induced voltage in the moving rod. If the
resistance in the circuit is 0.50 , find the current in the circuit. Find the amount
of energy dissipated by the resistor in one second. The source of energy that is
dissipated in the resistor is some external agent that keeps the bar moving at a
constant speed of 2 m/s by exerting an applied force F. Find the value of F. Ans:
0.25 V; 0.50 A; 0.13 J; 0.063 N
5. A 130 turn coil with a diameter of 2.1 cm is placed in a 0.0415 T magnetic field.
What is the magnetic flux through the coil? What is the value of the induced emf
if the magnetic field is reduced to zero in 50 msec? IF the coil has a resistance of
4 , what current flows through the coil as the magnetic field is reduced? Ans:
1.44 x 10-5 Wb; 0.0375 V; 0.0093 A
AP Lenz's Law Hand Rule Sample Problems
1. Draw the direction of the induced current.
2. Draw the direction of the induced current.
3. Draw the direction of the induced current.
4. Draw the direction of the induced current.
5. For the picture below, determihe the direction of the induced current when a. The
switch is opened and b. The switch is closed.
6. For the picture below, determine the direction of the induced current when a. The
switch is opened and b. The switch is closed.
7. Draw the direction of the induced current.
8. Draw the direction of the induced current.
9. For the picture below, what is the direction of the current through R caused by
current i in the wire below the loop?
10. What is the direction of the current in the loop pictured below?
11. The conducting bars are moved to the right, from position A to B, in the picture
below. The uniform magnetic field is directed outward. What is the direction of
the induced current in the loop?
12. The conducting bars are moved to the right, from position A to B, in the picture
below. The uniform magnetic field is directed inward. What is the direction of the
induced current in the loop?
AP Physics B - Magnetostatics Objectives
1. Forces on Moving Charges in Magnetic Fields:
o Students should understand the force experienced by a charged particle in
a magnetic field so they can:
1. 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.
2. Deduce the direction of a magnetic field from information about
the forces experienced by charged particles moving through that
field.
3. State and apply the formula for the radius of the circular path of a
charge that moves perpendicularly to a uniform magnetic field, and
derive this formula from Newton's Second Law and the magnetic
force law.
4. Describe the most general path possible for a charged particle
moving in a uniform magnetic field, and describe the motion of a
particle that enters a uniform magnetic field moving with specified
initial velocity.
5. Describe quantitatively under what conditions particles will move
with constant velocity through crossed electric and magnetic fields.
2. Forces on Current-carrying Wires in Magnetic Fields
o Students should understand the force experienced by a current in a
magnetic field so they can:
1. Calculate the magnitude and direction of the force on a straight
segment of current-carrying wire in a uniform magnetic field.
2. 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 consequency of these forces.
3. Fields of Long Current-carrying Wires
o Students should understand the magnetic field produced by a long straight
current-carrying wire so they can:
1. Calculate the magnitude and direction of the field at a point in the
vicinity of such a wire.
2. Use superposition to determine the magnetic field produced by two
long wires.
3. Calculate the force of attraction or repulsion between two long
current-carrying wires.
AP Physics B - Electromagnetism Objectives
1. Electromagnetic Induction:
o Students should understand the concept of magnetic flux so they can
calculate the flux of a uniform magnetic field through a loop of arbitrary
orientation.
o 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 square loop of wire pulled at a constant velocity into or
out of a uniform magnetic field.
 A loop of wire placed in a spatially uniform magnetic field
whose magnitude is changing at a constant rate.
 A loop of wire that rotates at a constant rate about an axis
perpendicular to a uniform magnetic field.
 A conducting bar moving perpendicular to a uniform
magnetic field.