Download Physics 1P22/1P92 Review Chapter 20 Electric

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Physics 1P22/1P92 Review
Chapter 20 Electric Forces and Fields
Key Concepts
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electric charge
principle of conservation of charge
charge polarization, both permanent and induced
good electrical conductors vs. good electrical insulators
Coulomb's law for the force exerted by one charged particle on
another
the electric field concept; representation of an electric field using
field lines or field vectors
electric field of a point charge (formula and field pattern, both for a
positive point charge and a negative point charge)
field pattern for a constant (i.e., uniform) electric field
field pattern for an electric dipole
properties of electric field lines in the vicinity of conductors (20.6)
Review Problems
CP 13 A small glass bead has been charged to +20 nC. A tiny ball
bearing 1.0 cm above the bead feels a 0.018 N downward electric
force. Determine the charge on the ball bearing.
Solution: Use Coulomb's law.
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The magnitude of the charge on the ball bearing is 10 nC. Because
the charge is attractive, and the charge on the glass bead is positive,
the charge on the ball bearing is negative. Thus, the charge on the
ball bearing is 10 nC.
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CP 59 A +10 nC charge is located at (x, y) = (0 cm, 10 cm) and
a 5.0 nC charge is located at (x, y) = (5.0 cm, 0 cm). Where would
a 10 nC charge need to be located in order that the electric field at
the origin be zero?
Solution: Let (x, y) represent the coordinates of the 10 nC charge.
The strategy is to write an expression for the total electric field at
the origin created by the three charges, then equate this expression
to zero, and solve for the unknown coordinates. Note the use of the
superposition principle.
The net electric field created by the three charges at the origin is
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CP 64 Two 3.0 g spheres on 1.0-m-long threads repel each other
after being equally charged, as shown in the figure. Determine the
charge q.
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Solution: Draw a free-body diagram for one of the spheres. I'll choose
to draw a free-body diagram for the sphere on the right:
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Chapter 21 Electric Potential
Key concepts:
• electric potential
• electric potential energy
• the electron-volt (eV), a convenient unit of energy when dealing with
atomic or subatomic phenomena
• electric potential formula for:
○ a point charge
○ a constant electric field
• connection between electric potential and electric field
• properties of equipotential surfaces
• properties of a conductor in electrostatic equilibrium
• capacitance
• capacitance of a parallel-plate capacitor
• capacitance of a parallel-plate capacitor with a dielectric medium
between the plates
• energy stored in an electric field
Review Problems
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Page 708, CP 66 An alpha particle and an antiproton are
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released from rest a great distance apart. They are oppositely
charged, so they accelerate towards each other. What are their
speeds when they are 2.5 nm apart?
Solution:
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Chapter 22 Current and Resistance
Key Concepts
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what is an electric current; the reality, and our simplified model
definition of current; "conventional current"
the principle of conservation of current; Kirchhoff's junction law
the "charge escalator" model of a battery
resistivity and resistance of a wire or other circuit element
Ohm's law
the ideal wire model for analyzing simple circuits
energy and power in simple circuits
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Review Problems
CP 41 The total charge a household battery can supply is
given in units of mA hr. For example, a 9.0 V alkaline battery is
rated at 450 mA hr, meaning that such a battery could supply
a 1 mA current for 450 hr, a 2 mA current for 225 hr, etc. How
much energy, in joules, is this battery capable of supplying?
Chapter 23 Electric Circuits
Key Concepts
• circuit diagrams; the symbols used to represent circuit
elements on circuit diagrams
• Kirchhoff's junction law; Kirchhoff's loop law
• series and parallel circuits
• equivalent resistance for a series circuit
• equivalent resistance for a parallel circuit
• analyzing simple circuits
• analyzing more complex circuits
• capacitors in series and parallel --- OMIT
Review Problems
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Chapter 24 Magnetic Fields and Forces
Key Concepts
• magnetic fields, magnetic field lines
• magnetic field patterns for a long straight wire, a circular loop, and a
solenoid
• using the formulas for the magnetic field for a long straight wire, a
circular loop, and a solenoid
• force exerted by a magnetic field on a moving charged particle
• possible paths of charged particles in magnetic fields
• applications: aurorae, flow meters, mass spectrometer
• force exerted by a magnetic field on a current-carrying wire
• magnetic force between parallel current-carrying wires
• torque exerted by a magnetic field on a current loop; electric motors
• OMIT Section 24.8
Review Problems
CP 50 An antiproton is moving in the combined electric and magnetic
fields shown in the figure.
(a) Determine the magnitude and direction of the antiproton's
acceleration at this instant.
(b) Repeat Part (a) if the direction of the velocity is reversed.
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Solution: The direction of the electric force on the antiproton is
upwards, and the direction of the magnetic force on the antiproton is
downwards. The magnitudes of the forces are calculated as follows:
(b) The magnetic force has the same magnitude as in Part (a) but is
now directed upwards. Thus, the net force on the antiproton is
CP 60 A mass spectrometer is designed to separate atoms of carbon to
determine the fraction of different isotopes. There are three main isotopes
of carbon, with the following atomic masses:
The atoms of carbon are singly ionized and enter a mass spectrometer
with magnetic field strength B = 0.200 T at a speed of 150 km/s. The
ions move along a semicircular path and exit through an exit slit. How
far from the entrance will the beams of the different isotope ions end
up?
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up?
Solution:
Thus, the distances for each of the three isotopes is
Chapter 25 Electromagnetic Induction and Electromagnetic Waves
Key Concepts
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electromagnetic induction; motional emf
magnetic flux
Faraday's law of induction
Lenz's law
electromagnetic waves
intensity and energy density of an electromagnetic waves
polarization of an electromagnetic wave
the electromagnetic spectrum
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Review Problems
CP 5 A 50 g horizontal metal bar, 12 cm long, is free to slide up and down
between two tall, vertical metal rods that are 12 cm apart. A 0.060 T
magnetic field is directed perpendicular to the plane of the rods. The bar is
raised to near the top of the rods, and a 1.0 Ohm resistor is connected
across the two rods at the top. Then the bar is dropped. Determine the
terminal speed at which the bar falls. Assume the bar remains horizontal
and in contact with the rods at all times.
Solution: The bar reaches terminal speed when the net force on it is zero.
This occurs when the downward gravitational force on the bar is balanced
by the upward magnetic force on the bar.
CP 17 The circuit in the figure is a square 5.0 cm on a side. The magnetic
field increases steadily from 0 T to 0.50 T in 10 ms. Determine the current in
the resistor.
Solution: First determine the induced emf.
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Is this induced emf in the same direction as the battery, or in the
opposite direction? Use Lenz's law to determine this.
CP 28 A radio antenna broadcasts a 1.0 MHz radio wave with 25 kW of
power. Assume that the radiation is emitted uniformly in all directions.
(a) Determine the wave's intensity 30 km from the antenna.
(b) Determine the electric field amplitude at this distance.
Solution:
CP 52 A 100-turn, 2.0-cm-diameter coil is at rest in a horizontal plane. A
uniform magnetic field 60 degrees away from vertical increases from 0.50
T to 1.50 T in 0.60 s. Determine the induced emf in the coil.
Solution:
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Only the component of the magnetic field PARALLEL to the axis of
the loop matters.
Chapter 26 Alternating Current
Key Concepts
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alternating current
peak quantities and rms quantities
electrical transformers
use of transformers to facilitate cross-country power transmission
household electricity
calculating the cost of electricity
biological effects and electrical safety
OMIT 26.5 to 26.7 inclusive
Review Problems
CP 10 A soldering iron uses an electric current in a wire to heat the tip. A
transformer with 100 turns on the secondary coil provides 50 W at an rms
voltage of 24 V.
(a) Determine the resistance of the wire in the soldering iron.
(b) Determine the number of turns in the primary coil.
(c.) Determine the current in the primary coil.
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Solution:
CP 12 A neon sign transformer has a 450 W AC output with an rms voltage
of 15 kV when connected to a normal household outlet. There are 500 turns
of wire in the primary coil.
(a) Determine the number of turns of wire in the secondary coil.
(b) Determine the current in both the primary and secondary coil when the
transformer is running at full power.
Solution:
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CP 20 The manufacturer of an electric table saw claims that it has a 3.0
hp motor. It is designed to be used on a normal 120 V outlet with a 15 A
circuit breaker. Is this claim reasonable? Explain.
Solution: Determine the maximum power possible from the normal
outlet:
The claim is not reasonable, because the circuit breaker will trip at a
maximum power of 2.4 hp. One would need a beefier circuit to
carry a larger current so that the saw could deliver 3 hp of power.
CP 24 A fisherman has netted a torpedo ray. As he picks it up, this electric
fish creates a short-duration 50 V potential difference between his hands.
His hands are wet with salt water, and so his skin resistance is a very low
100 Ohms. Determine the current that passes through his body and whether
the fisherman feels it.
Solution: From figures in the textbook, the total internal resistance of the
fisherman's two arms is 620 Ohms. Adding in the skin resistance to get the
total resistance, we obtain 720 Ohms. Thus, the current through the
fisherman is
Currents this large will definitely be felt. A brief pulse this large may
be harmless, but if it were prolonged it would be potentially lethal.
Chapter 28 Quantum Physics
Key Concepts
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• key puzzles leading to the introduction of quantum ideas: blackbody
radiation, photoelectric effect, atomic structure, atomic spectra
• Planck's introduction of the hypothesis that energy is collected in
bundles before being radiated by a glowing object
• Einstein's explanation of the photoelectric effect; the photon
hypothesis
• solving problems involving the photoelectric effect
• de Broglie's matter wave hypothesis; wave-particle duality
• quantization of energy for a bound particle; the "particle in a box," a
toy example
• energy levels for a bound particle; energy transitions ("quantum
jumps")
• Heisenberg's uncertainty principle
Review Problems
Chapter 28, CP 7 Electrons are emitted when a metal is
illuminated by light with a wavelength less than 388 nm but
for no greater wavelength. Determine the metal's work
function.
Solution:
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CP 8 Electrons in a photoelectric effect experiment emerge from a
copper surface with a maximum kinetic energy of 1.10 eV. Determine the
light's wavelength.
Solution: Look up the work function for copper; it is 4.65 eV.
CP 9 You need to design a photodetector that can respond to the entire
range of visible light. Determine the maximum possible work function of
the cathode.
Solution: The smallest desired frequency (which corresponds with the
largest desired wavelength) should be able to just eject electrons at the
maximum possible work function. Thus,
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Chapter 28, CP 11 Zinc has a work function of 4.3 eV. (a)
Determine the longest wavelength of light that will release
an electron from a zinc surface. (b) A 4.7 eV photon strikes
the surface and an electron is emitted. Determine the
maximum possible speed of the electron.
Solution:
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CP 15 The spacing between atoms in graphite is approximately 0.25 nm.
Determine the energy of an x-ray photon with this wavelength.
Solution:
CP 29 Determine the kinetic energy of an electron with a de Broglie
wavelength of 1.0 nm.
Solution:
CP 35 Determine the length of a box in which the minimum energy of an
electron in the n = 1 level has the same energy as a photon with a
wavelength of 600 nm.
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wavelength of 600 nm.
Solution: The energy of a photon with wavelength 600 nm is
The energy levels for a particle in a box are
For an electron in the n = 1 level, we obtain
Chapter 29 Atoms and Molecules
Key Concepts
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discrete atomic spectra; emission spectra, absorption spectra
the Geiger-Marsden experiment
Rutherford's atomic model
Bohr's atomic model
Bohr's model of a hydrogen atom
electron spin
quantum numbers for atomic electrons
Pauli exclusion principle and the periodic table
absorption and emission spectra of atoms
OMIT Sections 29.8 and 29.9
Review Problems
CP 8 The figure shows an energy level diagram for a simple atom.
Determine the wavelengths that appear in the atom's emission and
absorption spectra.
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Solution: For the emission spectrum, determine the energy differences:
Now calculate the corresponding photon wavelengths:
Only the first and third wavelengths appear in the absorption spectrum,
because atoms are ordinarily in their ground states. All three wavelengths
appear in the emission spectrum.
CP 9 An electron with kinetic energy 2.0 eV collides with an atom
whose energy-level diagram is the same as in the previous problem. (a) Is
the incident electron able to stimulate the atom to an excited state?
Explain. (b) If the answer to part (a) is yes, then determine the electron's
kinetic energy after the collision.
Solution: (a) Yes. Atoms are normally in their ground states, and it is
possible for the electron in the atom's ground state to absorb 1.5 eV of
energy from the incident electron to jump into the atom's n = 2 state.
(b) 2.0 eV
1.5 eV = 0.5 eV
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CP 19 Determine all possible wavelengths of photons that can be
emitted by transitions of electrons from the n = 4 level of a hydrogen
atom.
Solution:
CP 33 An electron with a speed of 5.00 × 106 m/s collides with an atom.
The collision excites the atom from its ground state (0 eV) to a state with
an energy of 3.80 eV. Determine the speed of the electron after the
collision.
Solution: Determine the initial kinetic energy of the electron. Then note
that the electron loses 3.80 eV of kinetic energy by transfer to the atom's
electron. Finally, use the remaining kinetic energy of the electron to
determine its final speed.
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The final kinetic energy of the electron is therefore 71.2
The corresponding final speed of the electron is
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3.8 = 67.4 eV.