Review Notes AP Physics B Electricity and Magnetism.
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Transcript of Review Notes AP Physics B Electricity and Magnetism.
![Page 1: Review Notes AP Physics B Electricity and Magnetism.](https://reader036.fdocuments.us/reader036/viewer/2022062518/56649e0e5503460f94af8a8b/html5/thumbnails/1.jpg)
Review Notes AP Physics B
Electricity and Magnetism
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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
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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.
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Constant UniformElectric 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
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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.
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Electric Field Inside Conductor
• The electric field is zero at all points inside a conductor in electrostatic equilibrium.
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• The electric field right at the surface of a charged conductor is perpendicular to the surface.
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• 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
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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)
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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
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• 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
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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.
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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.
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Ohm’s Law
• Raising resistance reduces current. • Raising voltage increases current. • We call this relationship Ohm’s Law
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Electrical Power
• Power is defined as
• And so work is qV• So P = qV/t• And
• So
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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.
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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
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Series Circuits Lab Summary
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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.
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Parallel Circuits Lab Summary
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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
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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
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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
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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)
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Measuring CapacitanceLet’s go back to thinking about plates!
V
QC
CVQ
C
VQ
ThereforeQE
difE
EdV
eCapacitancC
alityproportion ofcontant
constant,V
,
The unit for capacitance is the FARAD, F.
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Capacitor Geometry• The capacitance of a
capacitor depends on HOW you make it.
• It is a geometric property
d
AC
Nm
Cx
d
AC
A
CAC
o
o
2
212
o
o
1085.8
constantty permittivi vacuum
alityproportion ofconstant
platesbeteween distance d
plate of aread
1
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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.
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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
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Equivalent Capacitance –Parallel Circuits
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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
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Equivalent Capacitance –Series Circuits
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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.
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“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.
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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
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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.
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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.
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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.
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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
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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
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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
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• For a negative charge just put the force in the opposite direction
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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.
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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
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Force Between Two Current Carrying Wires
Two current carrying wires will interact with each other.
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Visualization
Parallel currents in the same direction attract
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Visualization
Parallel currents in the opposite direction repel
X
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Concept Check: Right Hand Rule
What is the direction of the force on the current carrying wire (green) in the magnetic field (red)?
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Concept Check• Which diagram correctly shows the magnetic field
inside and outside a current carrying loop of wire?
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Concept Check: Right Hand Rule
What is the direction of the force on the current carrying wire (green) in the magnetic field (red)?
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Concept Check: Right Hand Rule
What is the direction of the force on the current carrying wire (green) in the magnetic field (red)?
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Concept Check• Which diagram correctly shows the magnetic field
around a current carrying wire?
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Concept Check
What is the direction of the force on the proton shown below?
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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
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Faraday’s Law
– 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
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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
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Lenz’s LawWhen 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.
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Lenz’s Law
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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?
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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.
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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.