Download AP Physics Review Sheet 2 (Still Under Construction)

A.P. Physics Review Sheet 2
3/22/11
ELECTRICITY AND MAGNETISM
Electric Charge
 Charge is quantized with e = 1.60 x 10-19 C. Recall that you can use this as a conversion
factor with units 1.60 x 10-19 C/electron, for example.
 Electrons have a negative charge, –e, protons have a positive charge, +e, and neutrons are
electrically neutral.
 The SI unit of charge is the coulomb, C.
 Charge is conserved: The total charge in the universe is constant.
 Charge transfer occurs in two ways:
1. Charging through contact (ex. walking across a carpet, rubbing a balloon on your hair)
2. Charging by induction (recall electroscope demonstrations)
 Conductors, insulators, and semiconductors are compared in Table 1.
 A spherical distribution of charge, when viewed from the outside, behaves the same as an
equivalent point charge at the center of the sphere.
 A van de Graaff generator collects electric charge (recall demonstrations)
Table 1: Conductors, Insulators, and Semiconductors
Material Type
Description
Conductor:
Each atom gives up one or more electrons that are then free to
move throughout the material.
Insulator:
Does not allow electrons within it to move from atom to atom.
Semiconductor:
Has properties that are intermediate between those of insulators
and conductors.
Electric Force
 Electric charge, force, and field are compared in Table 2.
 Electric charges exert forces on one another along the line connecting them: Like charges
repel, opposite charges attract.
 Compare and contrast electric force to gravitational force (Law of Universal Gravitation):
1. Both forces are field forces
mm
2. Both are inverse square laws; recall that F  G 1 2 2 where G = 6.67 x 10-11 Nm2/kg2
r
3. Electric force is significantly stronger than gravitational force
4. Electric force can be attractive or repulsive whereas gravitational force is only attractive.
A.P. Physics Review Sheet 2, Page 2
Quantity
Table 2: Electric Charge, Force, and Field
Value or Equation
Electric Charge:
e = 1.60 x 10-19 C
Charge on an electron is –e.
Charge on a proton is +e.
Electric Force:
ur
ur
F  qo E
and
(The lower equation is called
Coulombs’s Law):
ur
q q
F  k o2
r
where
k  8.99 x 109 Nm2/C2
Electric Field:
ur
ur F
E
qo
V
s
Charge comes in quantized
amounts that are always
integer multiples of e.
Electric force is a
conservative force.
Superposition principle is
followed: the electric force on
one charge due to two or more
other charges is the vector
sum of each individual force.
1 N/C = 1 V/m
and
ur
q
Ek 2
r
E
Comments
(or V   Es )
Superposition principle is
followed: the total electric
field due to two or more
charges is given by the vector
sum of the fields due to each
charge individually.
Electric Field
 The electric field is the force per charge at a given location in space.
 The electric field vector, E , points in the direction experienced by a positive test charge.
 Electric field strength depends on charge and distance
 Electric fields can be represented by electric field lines. Rules for drawing electric field lines
are given in Table 3.
A.P. Physics Review Sheet 2, Page 3
Number
Table 3: Rules for Drawing Electric Field Lines
Rule
Rule 1:
Electric field lines point in the direction of the electric field
vector, E , at all times.
Rule 2:
Electric field lines start at positive charges or at infinity.
Rule 3:
Electric field lines end at negative charges or at infinity.
Rule 4:
Electric field lines are more dense the greater the magnitude of
E . In other words, for a set of point charges, the number of
electric field lines connected to each charge is proportional to
the magnitude of the charge.
Rule 5:
The electric field is always perpendicular to the equipotential
surfaces, and it points in the direction of decreasing (more
negative) electric potential (voltage).
Rule 6:
The electric field is perpendicular to the surface of a conductor.
Shielding and Charging by Induction
 Excess charge on a conductor, zero field within a conductor, shielding, and charging by
induction are compared in Table 4.
 Connecting a conductor to the ground is referred to as grounding. The ground itself is a good
conductor, and it can give up or receive an unlimited number of electrons.
 Charge tends to accumulate at sharp points on a conductor’s surface.
Concept
Table 4: Shielding and Charging by Induction
Description
Excess Charge on a
Conductor:
Excess charge placed on a conductor, whether positive or
negative, moves to the exterior surface of the conductor.
Zero Field within a
Conductor (Shielding):
The electric field within a conductor in equilibrium is zero.
Thus, a conductor shields a cavity within it from external
electrical fields.
Charging by Induction:
A conductor can be charged without direct physical contact with
another charged object. This is charging by induction.
A.P. Physics Review Sheet 2, Page 4
Electric Potential Energy
 The electric force is conservative, just like the force of gravity. As a result, there is a
potential energy U associated with the electric force.
 Electric potential energy shares many similarities with gravitational potential energy. For
example, U changes only in the direction parallel to the field whereas U  0 for
movement perpendicular to the field. (Recall that gravitational potential energy is zero
when an object moves sideways maintaining the same height off of the ground. The same is
true for a test charge that moves perpendicular to an electric field.)
 Electric potential energy and gravitational potential energy are compared in Table 5.
 The change in electric potential energy is defined by U  W , where W is the work done
by the electric field.
Table 5: Electric Potential Energy and Gravitational Potential Energy
Movement
Electric Potential Energy
( U  qo Ed )
Gravitational Potential
Energy ( U  mgh )
Charge or object moves a
small distance against the
field:
U electric
is small
U gravitational
is small
Charge or object moves a
large distance against the
field:
U electric
is large
U gravitational
is large
Charge or object maintains a
constant distance as it moves
perpendicular to the field:
U electric  0
U gravitational  0
Electric Potential = Potential Difference = Voltage
 The change in electric potential is defined by V  U / qo .
 The electric field is related to the rate of change of the electric potential. In particular, if the
electric potential changes by the amount V with a displacement s , the electric field in the
V
direction of the displacement is E  
.
s
 Electric potential energy and electric potential (voltage) are compared in Table 6.
 Electric potential energy and electric potential (voltage) for point charges are compared in
Table 7.
 For point charges, the electric potential forms a “potential hill” near a positive charge and a
“potential well” near a negative charge. See Fig. 20-5 (p.670) for related diagrams.
A.P. Physics Review Sheet 2, Page 5
Table 6: Electric Potential Energy and Electric Potential
Electric Potential (V)
(Also called Potential
Condition
Electric Potential Energy (U)
Difference or Voltage)
Test charge moves against the
electric field:
U  qo Ed
V 
Test charge moves in the
same direction as the electric
field:
U  qo Ed
V   Es
Test charge moves
perpendicular to the electric
field:
U  0
V  0
V 
U
 Es
qo
since
U
0

0
qo
qo
Table 7: Electric Potential Energy and Electric Potential for Point Charges
Quantity
Equation
Comments
Electric Potential Energy
for Point Charges:
U  0 when the separation
between the point charges qo
and q is infinite.
U  qoV
U
kqo q
r
k  8.99 x 10 Nm /C
9
Electric Potential (Voltage)
for Point Charges:
V
kq
r
2
2
Superposition principle is
followed: the total electric
potential energy of two or
more point charges is the sum
of the potential energies due to
each pair of charges.
V  0 at an infinite distance
from the point charge.
Superposition principle is
followed: the total electric
potential of two or more point
charges is the sum of the
potentials due to each separate
charge.
A.P. Physics Review Sheet 2, Page 6
Energy Conservation
 Since electric force is a conservative force, electric potential energies can be calculated, and
conservation of energy calculations can be performed.
 As usual, energy conservation can be expressed as K i  U i  K f  U f where equations for

the appropriate kinetic and potential energies appear in Table 8.
Positive charges accelerate in the direction of decreasing electric potential; negative charges
accelerate in the direction of increasing electric potential.
Energy Type
Table 8: Energy Conservation Calculations
Equation
Kinetic Energy:
K
Electric Potential Energy:
U  qoV
U
1 2
mv
2
kqo q
r
k  8.99 x 109 Nm2/C2
Comments
The moving particle is usually
a proton, electron, or point
charge.
(1)
When particles are
accelerated through a potential
difference, U  qoV is used.
(2) When point charges are
kq q
involved, U  o is used.
r
Work
 Table 9 shows how to calculate the work involved in moving charges within an electric field.
Type of Work
Table 9: Work Calculations
Equation
Comments
Work done BY an electric
field:
W  U
This comes from the definition
for a change in electric
potential energy.
Work you do to move a
charge AGAINST the field:
W  U  U f  U i
Recall that U f  0 when
charges are moved to infinity.
To calculate U i , sum the
electric potential energies due
to other charges within the
system.
A.P. Physics Review Sheet 2, Page 7
Capacitors
 A capacitor is a device that stores electric charge and electrical energy.
 A parallel-plate capacitor consists of two oppositely charged, conducting parallel plates
separated by a finite distance. The electric field is perpendicular to the plates, and it is
uniform in magnitude and direction.
 Table 10 compares the definition of capacitance, the capacitance of a parallel-plate capacitor,
the capacitance of a parallel-plate capacitor filled with a dielectric, and the electrical energy
stored in a capacitor.
Quantity
Table 10: Capacitance and Capacitors
Equation
Capacitance Definition:
C
Capacitance of a Parallelplate Capacitor:
C
o A
C
 o A
Capacitance of a Parallelplate Capacitor filled with
a Dielectric:
Electrical Energy Stored in
a Capacitor:
Comments
Capacitance is defined as the
amount of charge, Q , stored
in a capacitor per volt of
potential
difference,
V,
between the plates.
Q
V
where
d
 o  8.85 x 10-12 C2/Nm2
where
d
  dielectric constant from
Table 20-1.
1
1
Q2
U  QV  CV 2 
2
2
2C
o 
1
is the “permittivity
4 k
of free space.”
For us, a dielectric is an
insulating
material
that
increases the capacitance of a
capacitor.
In addition to storing charge, a
capacitor also stores electrical
energy.
A.P. Physics Review Sheet 2, Page 8
Electric Current





Q
where I is current in Amps (A), Q is
t
charge passing through a given area in Coulombs (C), and t is change in time in seconds
(s). By definition, 1 Amp is one Coulomb per second (1 A = 1 C/s).
By definition, the direction of the current I in a circuit is the direction in which positive
charges would move. The actual charge carriers, however, are generally electrons, which
move opposite in direction to I .
Drift velocity—net velocity of charge carriers (drift speed is relatively small; 68 min. on
average for an electron to travel 1.0 m)
Current sources
1. Batteries—change chemical energy into electrical energy
2. Generators—change mechanical energy into electrical energy
There are two types of current: Direct current (DC) and alternating current (AC).
Current is the rate of charge movement I 
Resistance
 When electrons move through a wire, they encounter resistance to their motion. In order to
move electrons against this resistance, it is necessary to apply a potential difference (voltage)
between the ends of the wire.
 Ohm’s Law is V  IR where V is potential difference (voltage) in Volts (V), I is current in
Amps (A), and R is resistance in Ohms (Ω).
 See Table 11 for a comparison of the electrical quantities in Ohm’s Law and their water
analogies.
 Ohmic versus nonohmic materials:
1. Ohmic materials have a constant resistance over a wide range of potential differences (ex.
most metals)
2. Nonohmic materials do not have a constant resistance over a wide range of potential
differences. (ex. diodes, which are analogous to check valves in plumbing)
 For an ohmic material, Ohm’s Law can be experimentally determined by plotting the current
(x-axis) against the voltage (y-axis). The equation for the resulting line is V  RI  0 where
the slope is the resistance, R , and the y-intercept is 0 since the line passes through the origin.
 Factors affecting resistance include length of conductor, cross-sectional area of a conductor,
conductor material, and temperature.
V L
 R 
where R is resistance in Ohms, V is potential difference (voltage) in Volts, I
I
A
is current in Amps,  is resistivity in Ohm-meters (See Table 21-1 on p.700), L is the length
of the conductor in meters, and A is the conductor’s cross-sectional area in m2.
 Resistors can be used to control the amount of current in a conductor. As resistance
increases, current decreases at constant voltage.
 Superconductors have no resistance below a critical temperature.
 Salt water and perspiration lower the body’s resistance.
A.P. Physics Review Sheet 2, Page 9
Table 11: Electrical Quantities in Ohm’s Law and Their Water Analogies
Electrical Quantity
Description
Unit
Water Analogy
Electric Potential
(Voltage)
Energy difference per
unit charge between
two points in a circuit.
Volt (V)
Water Pressure
Current
Amount of charge
flowing per unit time.
Ampere (A)
Amount of water
flowing per unit time.
Resistance
A measure of how
difficult it is for
electrical current to
flow in a circuit.
Ohm ()
A measure of how
difficult it is for water
to flow through a
pipe.
Electric Power
 Electric power, P , is the rate at which electrical energy is converted to other forms of
energy. It can be calculated using P  IV where P is power in Watts (W), I is current in
Amps (A), and V is potential difference (voltage) in Volts (V).
V2
2
 P  I R and P 
are both combinations of the power formula, P  IV , and Ohm’s
R
Law, V  IR .
 Most light bulbs are labeled with their electric power rating in Watts; the amount of heat and
light given off by the bulb is related to the power rating.
 Electric companies measure energy consumed in kilowatt hours (1 kWh = 3.6 x 106 J)
 Electrical energy is transferred at high potential differences (voltages) to minimize energy
loss.
Schematic Diagrams
 Make sure you can read, understand, and draw schematic diagrams.
 Know the symbols for wire, resistor, battery, open and closed switch, capacitor, bulb, and
plug.
 Be able to identify open circuits, closed circuits, and short circuits
 Short circuits occur when there is little or no resistance to the movement of charges; the
increase in current may cause the wire to overheat and start a fire.
 When a light bulb is screwed in, charges can enter through the base, move along the wire to
the filament, and exit the bulb through the threads.
 Light bulbs emit light because the filament is a resistor which converts some electrical
energy to light energy and heat energy.
 The electromotive force (emf) is the source of a circuit’s potential difference (voltage) and
electrical energy.
A.P. Physics Review Sheet 2, Page 10
Resistors in Series and Parallel Circuits
 Be able to use Ohm’s Law, V  IR , and the information in Table 12 to determine the
equivalent resistance, Req , current, I , and voltage V , for complex circuits containing both
series and parallel parts.
 For complex circuits containing batteries, Ohm’s Law, V  IR , is expressed as   I Battery Req
where  is the battery’s emf (voltage), I Battery is the current passing through the battery, and
Req is the circuit’s equivalent resistance.


In real life, batteries have a small internal resistance that must be included in calculations
when current is flowing. However, when current is not flowing like when a circuit switch is
open, this internal resistance is ignored.
Kirchoff’s rules in Table 13 are statements of charge conservation and energy conservation
as applied to closed electrical circuits. Kirchoff’s rules give an alternate way to find current
and voltage in complex circuits.
Quantity
Table 12: Series and Parallel Circuits
Series Circuit
Equivalent Resistance, Req :
Req  R1  R2  R3 
Current, I :
I  I1  I 2  I3 
Itotal  I1  I 2  I3 
Voltage, V :
(emf,  , when batteries are
involved)
Vtotal  V1  V2  V3  K  
V  V1  V2  V3  K  
Rule
 R
Parallel Circuit
1
1 1
1
   
Req R1 R2 R3

1
R
 I
Table 13: Kirchhoff’s Rules
Description
Junction Rule:
(Charge Conservation)
The algebraic sum of all currents meeting at a junction must
equal zero. Currents entering the junction are taken to be
positive; currents leaving the junction are taken to be negative.
Loop Rule:
(Energy Conservation)
The algebraic sum of all potential differences around a closed
loop is zero. The potential increases in going from the negative
to the positive terminal of a battery and decreases when
crossing a resistor in the direction of the current.
A.P. Physics Review Sheet 2, Page 11
Capacitors in Series and Parallel Circuits

For complex circuits containing multiple capacitors, capacitance, C 
Q
, is expressed as
V
QTotal
where  is the battery’s emf (voltage), QTotal is the circuit’s total charge, and

Ceq is the circuit’s equivalent capacitance.
 See Table 14 to determine equivalent capacitance, charge, and voltage for capacitors in series
and parallel circuits.
Ceq 
Quantity
Table 14: Capacitors in Series and Parallel Circuits
Series Circuit
Parallel Circuit
Ceq  C1  C2  C3 
 C
Equivalent Capacitance,
Ceq :
1
1
1
1
 
 
Ceq C1 C2 C3
Charge, Q :
Q  Q1  Q2  Q3 
Qtotal  Q1  Q2  Q3 
Voltage, V :
(emf,  , when batteries are
involved)
Vtotal  V1  V2  V3  K  
V  V1  V2  V3  K  

1
C
 Q
Resistor-Capacitor (RC) Circuits
 In circuits containing both resistors and capacitors, there is a characteristic time,   RC ,
during which significant changes occur. This time is referred to as the time constant. The
simplest such circuit, known as an RC circuit, consists of one resistor and one capacitor
connected in series.
 Table 15 gives equations describing the charge, electric potential (voltage), and current for a
capacitor in an RC circuit that is charging and discharging.
Ammeters, Voltmeters, and Multimeters
 Ammeters and voltmeters are devices for measuring currents and voltages, respectively, in
electrical circuits.
 Ammeters, voltmeters, and multimeters are compared in Table 16.
A.P. Physics Review Sheet 2, Page 12
Table 15: RC Circuit (One Resistor and One Capacitor Connected in Series)
The Capacitor is:
Quantity
Equation
Charging:
Charge, Q :
Q(t )  Qo (1  e t / )  C (1  e t / )
where   RC  time constant
Charging:
Potential, V :
V (t )  Vo (1  e  t / )
Charging:
Current, I :
 
I (t )  I o e t /    e t /
R
Discharging:
Charge, Q :
Q(t )  Qo et / where
  RC  time constant and the
circuit starts with charge Qo at
time t  0 .
Discharging:
Potential, V :
V (t )  Vo e  t /
Meter Type
Table 16: Ammeters, Voltmeters, and Multimeters
Connected in:
Ideal Case
Comments
Ammeter:
Series
Resistance is zero
Measures electric
current in Amps
Voltmeter:
Parallel
Resistance is infinite
Measures electric
potential in Volts
Multimeter:
Measures electric current in Amps, electric potential in Volts, and
resistance in Ohms depending on the instrument settings.
A.P. Physics Review Sheet 2, Page 13
Magnetic Field
 A magnet is characterized by two poles, referred to as the north pole and the south pole. All
magnets have both poles. Like poles repel and unlike poles attract.
 Magnetic fields can be represented with lines similar to the way electric fields can be
portrayed. In particular, the more closely spaced the lines, the more intense the magnetic
field.
 Magnetic field lines, which point away from north poles and toward south poles, always form
closed loops.
 The magnetic field of a bar magnet can be traced with a compass. The magnetic field lines
are drawn so that they point from the north magnetic pole to the south magnetic pole in the
direction the compass indicates.
 The Earth produces its own magnetic field. The geographic north pole of the Earth is
actually the south magnetic pole of the Earth’s magnetic field.
 Soft magnetic materials like iron are easily magnetized but tend to lose their magnetism
easily. For example, heating, cooling, or hammering iron promotes loss of magnetism.
 Hard magnetic materials like cobalt and nickel are difficulty magnetized, but once they are
magnetized, they tend to retain their magnetism.
Magnetic Force
 Table 17 compares magnetic force with electric force.
 In order for a magnetic field to exert a force on a particle, the particle must have charge and it
must be moving.
 The magnitude of the magnetic force is Fmagnetic  q vBsin  where Fmagnetic is in Newtons
(N), q is the magnitude of the charge in Coulombs (C), v is the speed of the charge in m/s,





B is the strength of the magnetic field in Tesla (T), and  is the angle between the velocity
vector v and the magnetic field vector B .
Table 18 gives the magnetic force right-hand rule and contrasts it with the magnetic field
right-hand rule.
Recall that for protons q = +1.60 x 10-19 C, and for electrons q = -1.60 x 10-19 C.
An electric current in a wire is caused by the movement of electric charges. Since moving
electric charges experience magnetic forces, it follows that a current-carrying wire will as
well.
See Table 19 to compare the magnetic force on moving charges, the magnetic force exerted
on a current-carrying wire, and the magnetic forces between current-carrying wires.
Wires that carry current in the same direction attract each other, and wires with oppositely
directed currents repel each other.
A.P. Physics Review Sheet 2, Page 14
Table 17: Comparison of Magnetic Force and Electric Force
Dependence
Magnetic Force
Electric Force
Depends on the charge of the
particle, q :
Yes
Yes
Depends on the magnitude of
the corresponding field:
Yes, it depends on the B field
Yes, it depends on the E field
Depends on the speed of the
particle, v :
Yes, which means that if No, static charged particles
v  0 , then Fmagnetic  0 . The have electric forces.
particle must be moving to
have a magnetic force.
Depends on the angle,  ,
between the velocity vector,
v , and the corresponding
field vector, B or E :
Yes
No
Corresponding Equation:
F magnetic  q vB sin 
F electric  qo E
where F magnetic is perpendicular to both v and B
Rule Name
Table 18: Right-Hand Rules for Magnetism
Rule
Magnetic Force Right-Hand
Rule:
The magnetic force, F magnetic , points in a direction that is
Magnetic Field Right-Hand
Rule:
The direction of the magnetic field produced by a current is
found by pointing the thumb of the right hand in the direction of
the current. The fingers of the right hand curl in the direction of
the field.
perpendicular to both v and B . For a positive charge, point the
fingers of your right hand in the direction of v and curl them
toward the direction of B . Your thumb points in the direction
of the magnetic force, F magnetic . The force on a negative
charge is in the opposite direction to that on a positive charge.
A.P. Physics Review Sheet 2, Page 15
Table 19: Comparison of Magnetic Forces
Magnetic Force Type
Equation
Comments
Magnetic Force on Moving
Charges:
F  q vB sin 
(1)
Particle must have a
charge and be moving to have
a magnetic force.
(2) F is perpendicular to
both v and B ; see magnetic
force right-hand rule.
Magnetic Force Exerted on a
Current-Carrying Wire:
F  ILB sin  where
L  wire length
F is perpendicular to both I
and B ; see magnetic force
right-hand rule.
Magnetic Forces between
Current-Carrying Wires:
o I1 I 2
L
where
2 d
o  4π x 10-7 Tm/A and
d  distance between wires
Wires that carry current in the
same direction attract one
another; wires that carry
current in opposite directions
repel one another.
F
Motion of Charged Particles in a Magnetic Field
 Table 20 compares the motion of a charged particle in an electric and a magnetic field.
 Table 21 compares constant-velocity straight-line motion, circular motion, and helical motion
for charged particles in a magnetic field.
 If a charged particle moves perpendicular to a magnetic field, it will orbit with a constant
mv
speed in a circle of radius r with r 
where r is in meters (m), m is the mass of the
qB
charge in kg, v is the speed of the charge in m/s, q is the magnitude of the charge in
Coulombs (C), and B is the strength of the magnetic field in Tesla (T),
Electric Currents, Magnetic Fields, and Ampere’s Law
 The key observation that serves to unify electricity and magnetism is that electric currents
cause magnetic fields. Hans Christian Oersted first discovered this in 1820 when he
observed that a compass needle deflected when electrical current flowed through a wire.
 Table 18 gives the magnetic field right-hand rule and contrasts it with the magnetic force
right-hand rule.
 Ampere’s Law
 Table 22 compares the magnetic field of a long straight wire, the magnetic field at the center
of a current loop, and the magnetic field of a solenoid.
A.P. Physics Review Sheet 2, Page 16
Table 20: Motion of a Charged Particle in an Electric Field and a Magnetic Field
Quantity Compared
Electric Field
Magnetic Field
Motion of a charged particle:
A charged particle in an A charged particle in a
electric field, E , accelerates magnetic field, B , accelerates
in the direction of the field.
perpendicular to both the
direction of the field and the
velocity, v .
Speed of the particle:
Speed changes; a charged
particle accelerates in the
direction of an electric field,
E.
Work done on the particle:
An electric field, E , can do A constant magnetic field, B ,
work on a charged particle.
cannot do work on a charged
particle because the magnetic
force is always perpendicular
to the velocity, v .
Speed is constant; a charged
particle accelerates perpendicular to both the direction of a
magnetic field, B , and the
velocity, v . Thus, the particle
changes direction rather than
velocity, which leads to circular motion at constant speed.
Table 21: Motion of Charged Particles in a Magnetic Field
Motion Type for Particle
Description
Constant Velocity, Straight- If a charged particle moves parallel or antiparallel to a
Line Motion:
magnetic field, it experiences no magnetic force since   0 .
Thus, its velocity remains constant.
Circular Motion:
If a charged particle moves perpendicular to a magnetic field, it
will orbit with a constant speed in a circle of radius r :
mv
r
qB
Helical Motion:
When a particle’s velocity has components both parallel and
perpendicular to a magnetic field, it will follow a helical path.
(Recall the double helix of DNA to remember what a helical
path means.)
A.P. Physics Review Sheet 2, Page 17
Electromagnetism and Magnetic Domains
 Use the second of our right-hand rules to determine the direction of a magnetic field around a
current-carrying wire. If the thumb of your right hand points in the direction of the current,
the fingers point in the direction of the magnetic field, B, around the wire.
 This right-hand rule can also be applied to a current-carrying loop to find the direction of the
magnetic field.
 A solenoid produces a strong magnetic field by combining several current-carrying loops. A
solenoid is helically wound coil of wire shaped like a Slinky.
Table 22: Comparison of Magnetic Fields
Magnetic Field Type
Equation
Comments
Magnetic Field of a Long,
Straight Wire:
B
o I
where
2 r
o  4π x 10-7 Tm/A
r  radial distance from wire
permeability of free
space, which has values of:
o  4π x 10-7 Tm/A or
o  1.26 x 10-6 Tm/A
Magnetic Field at the Center
of a Current Loop:
N o I
2R
N  number of loops
R  radius of loops
A single loop of current
produces a magnetic field
much like that of a permanent
magnet.
Magnetic Field of a Solenoid:
The magnetic field inside a
N
B  o   I  o nI
solenoid is nearly uniform and
L
aligned along the solenoid’s
N  number of loops
axis.
The magnetic field
L  length of solenoid
outside a solenoid is small,
n  number of loops per
and in the ideal case can be
length; n  N / L .
considered to be zero.
B
o 
Induced Current
 Electromagnetic induction means inducing a current with a changing magnetic field.
 Be able to explain the significance of electromagnetic induction in modern society.
 Methods for inducing an electromotive force (emf) in a current loop:
1. Moving the loop into or out of the magnetic field.
2. Rotating the loop within the magnetic field.
3. Changing the strength of the magnetic field through the static loop.
4. Altering the loop’s shape.
A.P. Physics Review Sheet 2, Page 18