Download Charge

Physics B
AP Review: Electricity and Magnetism
Charge (Q or q, unit: Coulomb)
Comes in + and –
The proton has a charge of e.
The electron has a charge of –e.
e = 1.602  10-19 Coulombs.
Name:________________
Note:
The electric field inside a conductor is always
zero, whether or not the conductor is charged or
near some external charges.
2.
Draw field around a + charge
Charge distribution
Positively charged objects have too few
electrons; negatively charged objects have
too many.
If the charged object is an insulator, the excess
charge is usually distributed evenly
throughout; if it is a conductor, the excess
charge will accumulate on the surface.
+
3.
Draw field around a - charge
Charge is conserved
In any nuclear reaction (or any process
whatsoever) total charge remains constant.
-
Charges apply force to each other
Like charges repel each other; unlike charges
attract each other
Coulomb’s Law
kq q
qq
1
F  12 2 or F  1 2 2 where k 
r
4 o r
4 o
Applies only to spherically symmetric charges
4.
Draw field around dipole
-
1. Coulomb’s Law (A-177 54)
Two isolated charges, + q and - 2q, are 2
centimeters apart. If F is the magnitude of the
force acting on charge -2q, what are the
magnitude and direction of the force acting on
charge + q ?
Magnitude
Direction
(A) 1/2 F
Toward charge —2q
(B) 1/2 F
Away from charge -2q
(C) F
Toward charge -2q
(D) F
Away from charge -2q
(E) 2F
Toward charge -2q
Show your work
5.
+
Draw field between capacitor plates
+++++++++++++++++++++++++
----------------------++
++
Magnitude
of the electric field
kq
q
1
E  +2 +or E 
where k 
r
4 o r 2
4 o
Applies only to spherically symmetric charges
Electric Fields (E, unit: N/C or V/m)
Start on + charges and terminate on – charges.
Electric field lines indicate direction force would be
on a tiny + test charge put in the field.
Electric field lines are not vectors. The field vectors
are tangent to the field lines.
Electric field vector gives direction of electric
force on a + charge placed in the field.
6/28/2017
Principle of Superposition
The electric field at a given point in space is the
vector sum of the electric fields due to all
charges in the vicinity.
The resulting vector gives the direction of the
electric force on a positive charge placed in the
field.
1
Bertrand
Electric Polarization
Electric fields cause polarization (redistribution of
charge) on neutral objects
Conductors are especially vulnerable to this effect.
When placed in an electric field, the charges
redistribute themselves so that the electric field
inside the conductor is zero.
Remember our electroscope experiments? The
electroscope is a conductor. When a charged
rod is brought near, the charges on the
electroscope move. That makes the vanes
separate, since they assume the same charge.
The electric field inside the electroscope’s metal
parts will be zero.
6. Field strength analysis (A177 20)
A hollow metal sphere of radius R is positively
charged. Of the following distances from the
center of the sphere, which location will have the
greatest electric field strength?
(A) O (center of the sphere)
(B) 3R/4
(C) 5R/4
(D) 2R
(E) None of the above because the field is of
constant strength
Explain your reasoning
7.
9. Electrical polarization (PAB)
Which of the following is true about the net
electric field inside an uncharged conducting
sphere in an external uniform electric field?
(A) It is exactly the same as the external field.
(B) It is in the same direction as the external
field, but is weaker.
(C) It is in a direction opposite to the field.
(D) It produces a torque on the sphere about the
direction of the field.
(E) It is zero.
Explain your reasoning by drawing a picture.
Electric Field (A177 57)
Charges +Q and -4Q are situated as shown
above. The net electric field is zero nearest
which point?
(A) A
(B) B
(C) C
(D) D
(E) E
Show your work:
10. Electrical field calculation from point
charges (A182 68)
8.
Electric Field (A187 17)
The diagram above shows an isolated, positive
charge Q. Point B is twice as far away from Q as
point A. The ratio of the electric field strength at
point A to the electric field strength at point B is
(A) 8 to 1
(B) 4 to 1
(C) 2 to 1
(D) 1 to 1
(E) 1 to 2
Show your work:
The figure above shows two particles, each with
a charge of +Q, that are located at the opposite
corners of a square of side d. What is the
direction of the net electric field at point P ?
A)
B)
C)
D)
Explain your reasoning:
6/28/2017
E)
2
Bertrand
Calculating Force from Field
F = Eq
the following occurs when the two spheres are
connected with a conducting wire?
(A) No charge flows.
(B) Negative charge flows from the larger sphere to the
smaller sphere until the electric field at the surface of
each sphere is the same.
(C) Negative charge flows from the larger sphere to the
smaller sphere until the electric potential of each
sphere is the same.
(D) Negative charge flows from the smaller sphere to the
larger sphere until the electric field at the surface of
each sphere is the same.
(E) Negative charge flows from the smaller sphere to the
larger sphere until the electric potential of each sphere
is the same.
11. Electric Force from Field (A177 17)
An electron is accelerated from rest for a time of
10-9 second by a uniform electric field that exerts
a force of 8.0 x 10-15 newton on the electron.
a) What is the magnitude of the electric field?
(A) 8.0 x 10-24N/C (B) 9.1 x 10-22 N/C
(C) 8.0 x 10-6N/C
(D) 2.0 x 10-5 N/C
(E) 5.0 x 104 N/C
Show your work
Explain your reasoning
b) The speed of the electron after it has
accelerated for the 10-9 second is most nearly
(A) 101 m/s
(B) 103 m/s
(C) 105 m/s
7
9
(D) 10 m/s
(E) 10 m/s
Show your work
Electrical Potential: spherical calculation
Calculates potential a given distance from charge.
kq
q
1
V
or V 
where k 
r
4 o r
4 o
Applies only to spherically symmetric charges
13. Electric Potential (PAB)
Electrical Potential (V, unit: Volt, V)
The electric potential is a scalar value related to
potential energy, which is also a scalar.
Potential gets more positive as you approach
positive charges. Mobile positive charges
therefore like to move to positions of lower
potential
Potential gets more negative as you near negative
charges. Mobile negative charges therefore
like to move to positions of higher potential
“Potential difference”, V, is usually more useful
than “absolute potential”, V.
Potential difference, V, is necessary for current
to flow.
A conducting sphere of radius R bears a positive
charge Q. What could the graph above represent
for that sphere?
(A) Electric potential as a function of distance from
the surface of the sphere.
(B) Electric potential as a function of distance from
the center of the sphere.
(C) Electric field as a function of the distance from
the surface of the sphere.
(D) Electric field as a function of the distance from
the center of the sphere.
(E) Charge as a function of distance from the center
of the sphere.
Explain your reasoning
12. Electric Potential (A182 70)
Two conducting spheres of different radii, as
shown above, each have charge - Q. Which of
6/28/2017
3
Bertrand
Electrical Potential: uniform field calculation
Electrical Potential in a uniform electric field
(that is, and electric field that is like the one
you drew in the capacitor above)
V = -Ed
Electrical Potential Energy
For absolute potential energy, U = qV
For potential energy change, U = qV
16. Electric Potential and Potential
Energy (S199 16)
An electron volt is a measure of
(A) energy
(B) electric field
(C) electric potential due to one electron
(D) force per unit electron charge
(E) electric charge
Explain your choice.
14. Electric Potential, Field, and Force
(A182 17)
Two large parallel conducting plates P and Q are
connected to a battery of emf , as shown above.
A test charge is placed successively at points I,
II, and III. If edge effects are negligible, the
force on the charge when it is at point III is
(A) of equal magnitude and in the same direction as
the force on the charge when it is at point I
(B) of equal magnitude and in the same direction as
the force on the charge when it is at point II
(C) equal in magnitude to the force on the charge
when it is at point I, but in the opposite direction
(D) much greater in magnitude than the force on the
charge when it is at point II, but in the same
direction
(E) much less in magnitude than the force on the
charge when it is at point II, but in the same
direction
17. Electric Potential and Potential
Energy (A187 18)
Explain your reasoning
The figure above shows two particles, each with
a charge of +Q, that are located at the opposite
corners of a square of side d. What is the
potential energy of a particle of charge +q that is
held at point P?
A) zero
B) 2 qQ/(4od)
C) qQ/(4od)
15. Parallel Plate E and V (PAB)
Two parallel conducting plates are connected
to a constant voltage source. The magnitude of
the electric field between the plates is 100 N/C.
If the voltage is doubled and the distance
between the plates is reduced to 1/4 the
original distance, the magnitude of the new
electric field is
(A) 40 N/C
(B) 80 N/C
(C) 100 N/C
(D) 400 N/C
(E) 800N/C
Show your work:
6/28/2017
D) 2 qQ/(4od)
E) 22 qQ/(4od)
Show your work
4
Bertrand
18. Charged conductor (S199 59)
A positive charge Of 10-6 coulomb is placed on
an insulated solid conducting sphere. Which of
the following is true?
19. Equivalent Capacitances (A182 15)
(A) The charge resides uniformly throughout the
sphere.
(B) The electric field inside the sphere is constant in
magnitude, but not zero.
(C) The electric field in the region surrounding the
sphere increases with increasing distance from
the sphere.
(D) An insulated metal object acquires a net positive
charge when brought near to, but not in contact
with, the sphere.
(E) When a second conducting sphere is connected by
a conducting wire to the first sphere, charge is
transferred until the electric potentials of the two
spheres are equal.
a) The equivalent capacitance for this network is
most nearly
(A) 10/7 uF
(B) 3/2 uF
(C) 7/3 uF
(D) 7 uF
(E) 14 uF
Show your work:
b) The charge stored in the 5-microfarad
capacitor is most nearly
(A) 360 uC
(B) 500 uC
(C) 710 uC
(D) 1,100 uC (E) 1,800 uC
Show your work:
Explain your reasoning:
Energy in a Capacitor
UE = ½ C (V)2
UE: electrical potential energy (J)
C: capacitance in (F)
V: potential difference between plates (V)
<< ADVANCED TOPIC >>
Capacitor
Consists of two “plates” (or conductors) in close
proximity. When the capacitor is “charged”,
there is a voltage across the plates, and they bear
equal and opposite charges.
20. Energy in a Capacitor (A187 70)
A 4 F capacitor is charged to a potential
difference of 100 V. The electrical energy stored
in the capacitor is
Capacitance (C, unit: Farad)
The ability of a capacitor to hold charge.
C = q / V
C: capacitance (F)
q: charge (on positive plate) (C)
V: potential difference between plates (V)
x 10-10 J
-4
(D) 2 x 10 J
(A) 2
x 10-8 J
-2
(E) 2 x 10 J
(B) 2
(C) 2
x 10-6 J
Show your work:
Drawing Capacitors in Circuits
Capacitance of parallel plate capacitor
Capacitance is related linearly with plate area,
and inversely with spacing between the plates
C = e0A/d
C: capacitance (F)
e: dielectric constant of filling
0 : electrical permittivity (8.85 x 10-12 F/m)
A: plate area (m2)
d: distance between plates (m)
Equivalent capacitance
The capacitance that a group of capacitors
together possesses.
For capacitors in series:
1/Ceq = Ci)
For capacitors in parallel:
Ceq = Ci
Equivalent capacitance equations are the
opposite of equivalent resistance equations.
6/28/2017
5
Bertrand
Usually internal resistance of the cell causes the
“terminal voltage” to be lower than the emf.
21. Parallel Plate Capacitor (A187 64)
Two parallel conducting plates, separated by a
distance d, are connected to a battery of emf  .
Which of the following is correct if the plate
separation is doubled while the battery remains
connected?
(A) The electric charge on the plates is doubled.
(B) The electric charge on the plates is halved.
(C) The potential difference between the plates
is doubled.
(D) The potential difference between the plates
is halved.
(E) The capacitance is unchanged.
Explain your reasoning
Conductors
Conduct electricity easily; i.e., metals.
Have low “resistivity”.
Insulators
Don’t conduct electricity easily; i.e. rubber.
Have high “resistivity”.
Resistivity ()
Depends on the identity of the material, not its
shape, size, or configuration.
Resistors (R, unit: ohm, )
Devices put in circuits to reduce the current:
The more a resistor reduces current, the higher
the resistance it provides to the circuit.
22. Parallel Plate Capacitor (1988)
14. The capacitance of a parallel-plate capacitor
can be increased by increasing which of the
following?
(A) The distance between the plates
(B) The charge on each plate
(C) The area of the plates
(D) The potential difference across the plates
(E) None of the above
Explain your reasoning
Calculating resistance (R) from resistivity ()
R = L/A
23. Calculating Resistance (PAB)
Wire from the same spool is
used to make two wire loops.
One loop has a radius b and
the other has a radius 2b. The
total resistance of the smaller
loop is R. What is the
resistance of the larger loop?
(A) R/4
(B) R/2
(C) R
(D) 2R
(E) 4R
Show your work or explain your reasoning
Current (I, unit: Ampere, A)
Flow of positive charge
I = Q/t
Direct Current (DC)
Uniform current flowing in one direction.
24. Calculating Resistance (A177 40)
The five resistors shown below have the lengths and
cross-sectional areas indicated and are made of
material with the same resistivity. Which resistor
has the least resistance?
Cell
What produces the current in a circuit:
Battery
Multiple cells in series. Below, for 2 cells:
Electromotive force (
The potential, or voltage, that can theoretically
be produced by the cell based on its chemistry.
6/28/2017
6
Bertrand
Explain your reasoning
Show your work
Ohm’s Law
V = IR
26. Power and Energy (A177 19)
An immersion heater of resistance R converts
electrical energy into thermal energy that is
transferred to the liquid in which the heater is
immersed. If the current in the heater is I, the
thermal energy transferred to the liquid in time t is
(A) IRt
(B) I2Rt
(C) IR2t
2
(D) IRt
(E) IR/t
Show your work
Ohmmeter
Placed across resistor or other circuit element to
measure resistance when no current is flowing.

Voltmeter
Placed across resistor or other circuit element to
measure potential change when current is flowing.
V
27. Power and Energy (A187 20)
A certain coffeepot draws 4.0 A of current when
it is operated on 120 V household lines. If
electrical energy costs 10 cents per
kilowatt-hour, how much does it cost to operate
the coffeepot for 2 hours?
(A) 2.4 cents
(B) 4.8 cents
(C) 8.0 cents
(D) 9.6 cents
(E) 16 cents
Show your work
Ammeter
Placed in a circuit in place of a wire to measure
the current flowing in that part of the circuit.
A
Power in Electrical Circuits (P, unit: Watt, W)
P = I V
Resistors in series
Energy in Electrical Circuits (unit: Joule, J)
E = (P)(t)
Note: the kilowatt hour is a unit of energy, not
a unit of power.
Req = Ri
Resistors in parallel
25. Power and Energy (A182 51)
The product
2 amperes x 2 volts x 2 seconds
is equal to
(A) 8 coulombs
(C) 8 joules
(E) 8 newton-amperes
6/28/2017
1/Req = Ri)
(B) 8 newtons
(D) 8 calories
7
Bertrand
28. Equivalent Resistance (S195 18)
Show your work or state your reasoning
30. General Circuit Problems (A182 20)
Parts a-c relate to the following circuit diagram,
which shows a battery with an internal resistance
of 4.0 ohms connected to a 16-ohm and a
20-ohm resistor in series. The current in the
20-ohm resistor is 0.3 amperes.
Which two arrangements of resistors shown above
have the same resistance between the terminals?
(A) I and II
(B) I and IV
(C) II and III
(D) II and IV
(E) III and IV
Show your work
a) What is the emf of the battery?
(A) 1.2 V
(B) 6.0 V
(D) 12.0 V
(E) 13.2 V
Show your work
(C) 10.8 V
29. Equivalent Resistance (A177 15)
A
C
B
b) What is the potential difference across the
terminals X and Y of the battery?
(A) 1.2 V
(B) 6.0 V
(C) 10.8 V
(D) 12.0 V
(E) 13.2 V
Show your work
a) The total equivalent resistance between points
X and Y in the circuit shown above is
(A) 3 
(B) 4 
(C) 5 
(D) 6 
(E) 7 
Show your work
c) What power is dissipated by the 4-ohm
internal resistance of the battery?
A) 0.36 W
(B) 1.2 W
(C) 3.2 W
(D) 3.6 W
(E) 4.8 W
Show your work
b) When there is a steady current in the circuit,
the amount of charge passing a point per unit of
time is
(A) the same everywhere in the circuit
(B) greater at point X than at point Y
(C) greater in resistor A than in resistor B
(D) greater in resistor B than in resistor C
(E) greater in resistor B than in resistor A
6/28/2017
8
Bertrand
33. Kirchoff’s Rules (A182 14)
Kirchhoff's loop rule for circuit analysis is an
expression of which of the following?
(A) Conservation of charge
(B) Conservation of energy
(C) Ampere's law
(D) Faraday's law
(E) Ohm's law
Explain your reasoning
31. Circuit Problem (A182 50)
In the diagrams above, resistors R1. and R2 are
shown in two different connections to the same
source of emf  that has no internal resistance.
How does the power dissipated by the resistors
in these two cases compare?
(A) It is greater for the series connection.
(B) It is greater for the parallel connection.
(C) It is the same for both connections.
(D) It is different for each connection, but one must know
the values of . R1 and R2 to know which is greater.
(E) It is different for each connection, but one must know
the value of  to know which is greater.
Explain your reasoning
Magnetic Dipole
Magnetic field lines are
complete loops that exit the
magnet at the north pole and
re-enter at the south pole.
Magnetic Field (B-field)
Units
Tesla (SI)
Gauss (1 T = 104 gauss)
Magnetic Monopoles
Do not exist!
32. Ohm’s Law (A177 68)
Magnetic Force on Charged Particle
F = qvBsin
direction: Right Hand Rule
34. Magnetic Force (A187 22)
In the circuit shown above, the value of r for
which the current I is 0.5 ampere is
(A) 0 
(B) 1 
(c) 5 
(D) 10 
(E) 20 
Show your work
An electron is in a uniform magnetic field B that
is directed out of the plane of the page, as shown
above. When the electron is moving in the plane
of the page in the direction indicated by the
arrow, the force on the electron is directed
(A) toward the right
(B) out of the page
(C) into the page
(D) toward the top of the page
(E) toward the bottom of the page
State your reasoning
Kirchoff’s 1st Rule (Junction rule)
The sum of the currents entering a junction
equals the sum of the currents leaving the
junction. Conservation of charge.
Kirchoff’s 2nd Rule (Loop rule)
The net change in electrical potential in going
around one complete loop in a circuit is equal
to zero. Conservation of energy.
6/28/2017
9
Bertrand
Magnetic Fields
are formed by moving charges.
may exert a force on moving charges, provided a
portion of the velocity is perpendicular to the
field.
B directed into paper
E directed down
Velocity of charged particle directed right
q
Magnetic Forces can...
accelerate charged particles by changing their
direction, causing charged particles to move
in circular or helical paths
Magnetic Force on Current-carrying Wire
F = I L B sin
Magnetic Forces cannot...
change the speed or kinetic energy of charged
particles, or do work on charged particles
36. Magnetic Force (A177 47)
The magnetic force is centripetal
qvBsin = mv2/r
qB = mv/r
A wire in the plane of the page carries a current I
directed toward the top of the page, as shown
above. If the wire is located in a uniform
magnetic field B directed out of the page, the
force on the wire resulting from the magnetic
field is
(A) directed into the page
(B) directed out of the page
(C) directed to the right
(D) directed to the left
(E) zero
State your reasoning
35. Magnetic Force as a Centripetal Force
(PAB)
A magnetic field of Bo forces a proton to move
in a circle of radius R. The plane of the circle is
perpendicular to the magnetic field.
a) Of the following, which best represents the
amount of the work done by the magnetic field on
the proton during one complete orbit of the circle?
(A) 0 J (B) BoR (C) Bo/R
(D) qvBR
(E) Must know the speed of the particle.
Show your work or explain your reasoning
37. Magnetic Force (S195 63)
Two long, parallel wires, fixed in space, carry
currents I1 and 12. The force of attraction has
magnitude F. What currents will give an
attractive force of magnitude 4F?
1
1
(A) 2 I 1 and I 2
(B) I 1 and I 2
4
2
1
1
(C) I 1 and I 2
(D) 2 I 1 and 2 I 2
2
2
4 I and 4 I 2
(E) 1
Show your work
b) Of the following, which is the best estimate of
the speed of the proton as it moves in the circle?
(A) c
(B) BR/m
(C) eBR/m
(D) eBR2/m
(E) None of the above.
Show your work
Velocity filter
Electric and magnetic fields can be used together
to precisely select the velocity of a charged
particle.
6/28/2017
10
Bertrand
Magnetic Field for Long Straight Wire
B = oI/(2r)
39. Magnetic Flux (A187 19)
38. Magnetic Field (A182 19)
A rectangular wire loop is at rest in a uniform
magnetic field B of magnitude 2 T that is directed
out of the page. The loop measures 5 cm by 8 cm,
and the plane of the loop is perpendicular to the
field, as shown above. The total magnetic flux
through the loop is
(A) zero
(B) 2 x 10-3 Tm
-3

(C) 8 x 10 Tm
(D) 2 x 10-1 Tm
-1

(E) 8 x 10 Tm
Show your work
Two long, parallel wires are separated by a
distance d as shown above. One wire carries a
steady current I into the plane of the page
while the other wire carries a steady current I
out of the page. At what points in the plane of
the page and outside the wires, besides points
at infinity, is the magnetic field due to the
currents zero?
(A) Only at point P
(B) At all points on the line SS'
(C) At all points on the line connecting the two
wires
(D) At all points on a circle of radius 2d centered
on point P
(E) At no points
Explain your reasoning
Induced Current
A system will respond to oppose changes in
magnetic flux.
Changing the magnetic flux can generate
electrical current.
Faraday’s Law of Induction
 = -NB/t
Hand Rule for magnetic force on moving positive charge
Place fingers in direction of velocity. Then rotate your wrist
so that your fingers can bend into the direction of the field.
Your thumb gives direction of the force.
Hand Rule for magnetic force on moving negative charge
Use the method described above, then flip your thumb 180o.
Alternately, you may use your left hand.
To generate voltage
 = -B/t
 = -(BAcos)/t
Change B, Change A, or Change 
Hand Rule for magnetic force on current in wire
Place fingers in direction of current. Then rotate your wrist so
that your fingers can bend into the direction of the field. Your
thumb will be pointing in the direction of the force.
40. Faraday’s Law (A187 66)
Hand Rule for fields where current is straight
Curve your fingers. Place thumb in direction of current. Your
curved fingers point in direction of curved magnetic field.
Hand Rule for fields where current is circular
Curve your fingers. Place curved fingers in direction of
current. Your thumb points in direction of magnetic field in
center of circular current.
Magnetic Flux (B, unit Webber, Wb)
The product of magnetic field and area.
B = BAcos
B: magnetic flux in Webers (Tesla meters2)
B: magnetic field in Tesla
A: area in meters2.
: angle between area and magnetic field.
6/28/2017
A uniform magnetic field B that is perpendicular
to the plane of the page passes through two
loops, as shown above. The field is confined to a
region of radius a, where a < b, and is changing
at a constant rate. The induced emf in the wire
loop of radius b is  . What is the induced emf in
the wire loop of radius 2b ?
11
Bertrand
(A) Zero
 2
(E) 4
(B)
(C) 
Explain your reasoning
(D) 2
Show your work or explain your reasoning
41. Faraday’s Law (A182 67)
A square loop of wire of resistance R and side a
is oriented with its plane perpendicular to a
magnetic field B. as shown above. What must be
the rate of change of the magnetic field in order
to produce a current I in the loop?
(A) IR/a2
(B) la2/R
(C) la /R
(D) Ra/l
(E) IRa
Show your work
Lenz’s Law
Induced current will flow in a direction so as to
oppose the change in flux.
43. Lenz’s Law (PAB)
A single circular loop of wire in the plane of the
page is perpendicular to a uniform magnetic field
B directed out of the page, as shown above. If
the magnitude of the magnetic field is increasing,
then the induced current in the wire is
(A) directed upward out of the paper
(B) directed downward into the paper
(C) clockwise around the loop
(D) counterclockwise around the loop
(E) zero (no current is induced)
Explain your reasoning
Motional emf
Faraday’s law can be used to show that a wire
moving in a magnetic field generates a
potential equivalent to
 = BLv
42. Motional emf (A182 41)
A wire of constant length is moving in a constant
magnetic field, as shown above. The wire and
the velocity vector are perpendicular to each
other and are both perpendicular to the field.
Which of the following graphs best represents
the potential difference  between the ends of the
wire as a function of the speed v of the wire?
6/28/2017
12
Bertrand