Review Notes AP Physics B
Electricity and Magnetism
Electric Fields
• The electric field around a source charge will be
different at different locations around the
charge.
– Further away from the charge, the magnitude
of the force will decrease. We know this from
Coulomb's law
• The direction will also be different
Electric Field Lines
• The electric field will show up as arrows drawn at
various points around charged objects.
• These electric field lines (or electric force
lines)are drawn below for two simple examples: a
negative and positive source charge.
Constant Uniform
Electric Field Lines
• Constant, uniform electric
field lines can be created
with parallel plates of
different charges
• There’s slight curvature at
the end, but this is often
ignored since it is ofen
small compared to the
length of the plate
Force on a charge in an
electric field
• If a charged particle q is
placed in a region where
there is an electric field is
E:
– The direction of F is the
same as the direction of
E if q is positive.
– The direction of F is
opposite to the direction
of E if q is negative.
Electric Field Inside Conductor
• The electric field is zero at all points
inside a conductor in electrostatic
equilibrium.
• The electric field right at the surface of a
charged conductor is perpendicular to
the surface.
• At the top the charge has maximum
electrical potential energy
• If you release the charge it will
accelerate downward
• While it falls electrical potential energy
-> kinetic energy
• When it reaches the negative plate
(reference point) it has no electrical
potential energy, it’s all kinetic
Voltage –Relation to
Electrical Potential Energy
• Voltage is the change in electric
potential energy per unit charge
• Many names: electric potential
difference, electric potential, potential
difference (and voltage)
Voltage
• The potential difference from one point, A,
to another point, B, is the work done against
electrical forces in carrying a unit positive
test charge from A to B.
• Represent potential difference by V=VB-VA
– Units: Volts = joules/coulomb (work per charge)
• The work done in transporting charge q
from A to B is
– W = q(VB-VA )=qV
• The electric potential V at a point in space
is the sum of the potentials due to each
charge because it is a scalar
• The electric potential, like the electric field,
obeys the principle of superposition
Electron Volts
• Define one electron volt as the energy needed to
move one electron through one volt of potential
difference
• If you need to do a calculation of energy in electron
volts, you just figure out how many elementary
charges you have multiplied by the voltage they
moved through.
What is the conventional current and
why?
• Conventional current is the flow of positive
charges flowing from the positive to the
negative terminal.
• Historically, positive charges were identified
as the ones that flowed in the circuit.
Ohm’s Law
• Raising resistance reduces current.
• Raising voltage increases current.
• We call this relationship Ohm’s Law
Electrical Power
• Power is defined as
• And
• So P = qV/t
• And
• So
so work is qV
What affects the resistance of a
conducting wire?
• Decreasing the length of a wire (L) or
increasing the cross- sectional area (A) would
increase conductivity.
• Also, the measure of a conductor's resistance
to conduct is called its resistivity. Each
material has a different resistivity.
Series Circuit Lab Summary
• The current passing through all parts of a
series circuit is the same.
Itotal = I1 = I2 = I3
• The sum of the voltage drops across each of
the resistors in a series circuit equals the
voltage of the battery.
Vtotal = V1 + V2 + V3 +…
• Show, using these facts and Ohm’s Law,
what the equivalent resistance is
Series Circuits Lab Summary
Vtotal = V1 +V2 +V3
Since V = IR
Þ I total Rtotal = I1 R1 + I 2 R2 + I 3 R3
Since Itotal = I1 = I 2 = I3
Þ IRtotal = IR1 + IR2 + IR3
Þ Rtotal = R1 + R2 + R3
Parallel Circuits Lab Summary
• The sum of the currents through each of the
resistors in a parallel circuit equals the
current of the battery.
Itotal = I1 + I2 + I3…
• The voltage across all the resistors in a
parallel circuit is the same.
Vtotal = V1 = V2 = V3…
• Show, using these facts and Ohm’s Law, what
the equivalent resistance is.
Parallel Circuits Lab Summary
I total = I1 + I 2 + I 3
V
Since I =
R
Vtotal V1 V2 V3
Þ
= + +
Rtotal R1 R2 R3
Since Vtotal = V1 = V2 = V3
1
1 1 1
Þ
= + +
Rtotal R1 R2 R3
Kirchhoff's Rules
• Kirchhoff's First rule, or junction rule is based
on the law of conservation of charge. It states:
• At any junction point, the sum of all currents
entering the junction point must equal the
sum of all the currents exiting the junction.
• For example
• I3 = I1 + I2
Kirchhoff's Rules
• Kirchhoff's Second rule, or loop rule is based
on the law of conservation of energy. It states:
• The sum of all changes in potential around any
closed path must equal zero.
• For example
V = V1 + V2
EMF
• A battery is a source of voltage AND a
resistor.
• Electromotive force (EMF) is the
process that carries charge from low to
high voltage.
• Another way to think about it is that
EMF is the voltage you measure when
no resistance is connected to the
circuit.
• The terminal voltage (at the terminals
of the battery when current flows is
found : VT =E-Ir
Capacitance
• Capacitance reflects the ability of a capacitor to
store charge
• In the picture below, the capacitor is symbolized by a
set of parallel lines.
• Once it's charged, the capacitor has the same voltage
as the battery (1.5 volts on the battery means 1.5 volts
on the capacitor)
Measuring Capacitance
Let’s go back to thinking about plates!
The unit for capacitance is the FARAD, F.
V  Ed ,
V E , if d  constant
E Q Therefore
Q V
C  contant of proportion ality
C  Capacitanc e
Q  CV
Q
C
V
Capacitor Geometry
• The capacitance of a
capacitor depends on
HOW you make it.
• It is a geometric property
1
C A C 
d
A  area of plate
d  distance beteween plates
A
C
d
 o  constant of proportion ality
 o  vacuum permittivi ty constant
 o  8.85 x10
C
o A
d
12
C2
Nm 2
Capacitance
• When a battery is connected to a
capacitor, charge moves between
them. Every electron that moves to
the negative plate leaves a positive
nucleus behind.
• As the plates charge, the potential
difference between the places
increases.
• The current through the circuit
decreases until the capacitor
becomes fully charged.
Equivalent Capacitance –Parallel Circuits
• The voltage across each
capacitor is the same.
V = V1 = V2
• The total charge is the
sum of the charge on all
the capacitors.
Q = Q1 + Q2
Equivalent Capacitance –Parallel Circuits
Q total = Q1 + Q2 + Q3
Since Q = CV
Þ CtotalVtotal = C1V1 + C2V2 + C3V3
Since Vtotal = V1 = V2 = V3
Þ CtotalV = C1V + C2V + C3V
Þ Ctotal = C1 + C2 + C3
Equivalent Capacitance –Series Circuits
• The sum of the voltage
drops across each of the
resistors in a series circuit
equals the voltage of the
battery.
V = V1 + V2
• The charge on each
capacitor is the same.
Q = Q1 = Q2
Equivalent Capacitance –Series Circuits
Vtotal = V1 + V2 +V3
Q
Since V =
C
Qtotal Q1 Q2 Q3
Þ
= + +
Ctotal C1 C2 C3
Since Q total = Q1 = Q2 + Q3
Þ
1
Ctotal
1 1
1
= + +
C1 C2 C3
Magnetic Fields
• Magnetic fields can be visualized using
magnetic field lines, which are always closed
loops.
• Magnetic fields
are always drawn
coming out of the
north pole and
going into the
south pole.
• The more lines per
unit area, the
stronger the field.
“B”
• The magnetic field is often expressed as B.
• The field is a vector and has both magnitude
and direction.
UNITS
• The SI unit of B is the tesla, T.
• The gauss, G, is common as well
1 G =10-4 T
• To gain perspective, the weak magnetic field
of the Earth at its surface is around 0.5 x 10-4
T or simply 0.5 G.
Current-Carrying Wire
• A current-carrying wire produces a magnetic
field around the wire
– Concentric circles in plane perpendicular to the
wire represent the magnetic field graphically
– Compass needles align tangent to arcs of the
magnetic field lines circling a current-carrying
wire, indicated direction of field
– Get direction of field from right hand rule
The Right Hand Rule
• The direction of the field
is given by a right-hand
rule.
• First, orient your right
hand thumb in the
direction of the current...
• Then wrap your fingers
in the direction of the B
Field.
Magnetic Field: The 3rd Direction
• Picture the field line like an arrow. The head of
the arrow is the direction of the field.
• If the magnetic field is into the page, you will
see the tail of the arrow.
• If the magnetic field is out of the page, you will
see the front of the arrow.
Force on electric current in a magnetic
field
• A magnet exerts a force on a current-carrying
wire. The direction of the force is given by
another different right-hand rule.
• The force on the wire depends on the
current, the length of the wire, the magnetic
field, and its orientation.
• This equation defines the magnetic field, B.
Right Hand Rule -Flat
• Orientate your thumb so
it’s in the direction on
the current
• Point your palm in the
direction the force
• Your fingers point in the
direction of the magnetic
field
Force on Electric Charge Moving in
Magnetic Field
• The magnitude of force of a magnetic field of
strength B on a single moving charge q, is a
function of the velocity of the particle v, and
its angular orientation
• Force maximum when velocity and current are
perpendicular and 0 N when they are parallel
Right Hand Rule -Flat
• Orientate your thumb so
it’s in the direction of the
velocity (and current!)
• Point your palm in the
direction the force
• Your fingers point in the
direction of the magnetic
field
• For a negative charge just put the force in the
opposite direction
Force on an
Electric Charge
Moving in a
Magnetic Field
If a charged
particle is
moving
perpendicular to
a uniform
magnetic field,
its path will be a
circle.
Magnetic Field Due to a Straight Wire
• The strength of magnetic field due to
a long straight wire is proportional to
the current in the wire I, and
inversely proportional to the distance
from the wire r
• Where the permeability of free space
is
Force Between Two Current Carrying Wires
Two current carrying wires will interact with each other.
Visualization
Parallel currents in the same direction attract
Visualization
Parallel currents in the opposite direction repel
X
Concept Check: Right Hand Rule
What is the direction of the force on the current
carrying wire (green) in the magnetic field (red)?
Concept Check
• Which diagram correctly shows the magnetic field
inside and outside a current carrying loop of wire?
Concept Check: Right Hand Rule
What is the direction of the force on the current
carrying wire (green) in the magnetic field (red)?
Concept Check: Right Hand Rule
What is the direction of the force on the current
carrying wire (green) in the magnetic field (red)?
Concept Check
• Which diagram correctly shows the magnetic field
around a current carrying wire?
Concept Check
What is the direction of the force on
the proton shown below?
Faraday’s Law
• Any change in the magnetic environment of a
coil of wire will cause a voltage (emf) to be
"induced" in the coil.
• Changes could come from anything
– Changing magnetic field strength
– Moving magnet w.r.t. the coil
– Moving the coil w.r.t. a magnetic field
– Rotating the coil relative to the magnetic field
Faraday’s Law
D ( BA)
DFm
e = -N
=Dt
Dt
– where N = number of turns (always 1 on AP B)
– Φ = BA = magnetic flux
– B = the external magnetic field
– A = area of the coil
• On the equation sheet
Magnetic Flux
• Magnetic flux is the product of the average magnetic
field times the perpendicular area that it penetrates.
• The area must be perpendicular to the magnetic field.
• SI Unit = Weber (Wb) or Volt/s
• Since we model a magnetic field with field line, you
can think of flux as the number of field lines passing
through a given area
Lenz’s Law
When an emf is generated by a change in magnetic
flux according to Faraday's Law, the polarity of the
induced emf is such that it produces a current
whose magnetic field opposes the change which
produces it.
Lenz’s Law
Lenz’s Law
Practice
The conducting
rectangular loop falls
through the magnetic
field shown. What
direction is the
conventional current
induced in the loop
as it leave the field?
Lenz’s Law Practice
A circular wire loop
sits inside a larger
circular loop that is
connected to a
battery as shown.
Determine the
direction of the
convention current
induced in the inner
loop when the switch
in the outer circuit is
closed.
Lenz’s Law Practice
• A circular wire loop
sits below a falling
magnet as shown.
Determine the
direction of the
conventional current
induced in the loop as
the magnet
approaches the loop.