Physics 112 Midterm Exam - Questions & Verified Answers
If two objects both have more of the positive type of charge then the objects will repel each other.
than negative (usually referred to as a positive net charge)
If two objects both have more of the negative type of then the objects will repel each other.
charge than positive (referred to as a negative net charge)
If one object has more of the positive type of charge and then the objects will attract each other.
one object has more of the negative type of charge
If a material gains electrons the material will have a negative net charge
If a material loses electrons the material will have a positive net charge.
A particular object has a net 6.5 μC of the positive type of Since the object has extra of the positive type of charge, electrons must have been
charge. Were electrons transferred onto or off the object? transferred off the material. Since electrons carry the negative type of charge,
How many? removing electrons would have left behind more positive than negative.
The total amount of charge moved off the material was 6.5 μC. Each electron
moved off carries 1.6x10-19 C. Convert μC into C and divide.
6.5x10-6 C / 1.6x10-19 C = 4.06x1013 electrons were removed.
Solve for the number of charge carrier particles (protons or The amount of charge carried by one electron is 1.6x10-19 C. Divide the total
electrons) transferred on or off the object. charge by the charge of one electron to solve for the number of electrons.
(3.5x10-6 C) / (1.6x10-19 C) = 2.25x1013 electrons were transferred off the object.
conductors Materials that allow electrons to move easily through them. Metals are good
conductors
insulators Materials that do not allow electrons to move freely through them. Nonmetals are
good insulators
Semiconductors are a class of materials that, as you might expect, share properties of both.
Conduction is the movement of charge from one object to another. It is easy to move charge
from metal to metal (conductor to conductor) but much more difficult to move charge
from insulator to insulator.
The transfer of charge caused by rubbing two objects against each other is a
special type of conduction called triboelectric charging.
An electroscope is a device that has small gold foil strips The negative charge on the rod repels the negative charge already present in the
suspended from a metal rod. If a negatively charged rod is electroscope. Since the electroscope is made from metals, electrons will be pushed
brought near the top of a neutral electroscope, the gold foil down into the gold strips. The electroscope is now polarized (the top is more
strips will separate. (See below.) Explain why this positive, and the bottom is more negative). However, the relocated negative charge
happens. now in the thin gold strips will repel each other causing the gold strips to separate.
Induction is a charge transfer process that involves polarizing an object and then allowing
charge to transfer to another object through conduction. While still under the
influence of the dipole, the charge transfer mechanism is removed (the two objects
are moved apart). The two objects are now charged.
, Physics 112 Midterm Exam - Questions & Verified Answers
Polarization is a redistribution of charge rather than a transfer of charge; the total amount of
charge on the polarized object does not change.
static electric force Proportional to the quantity of net charge on both objects, and proportional to the
inverse-square of the distance between the two charged objects.
In other words:
Fe α q1q2 / r2
Where Fe is the force, q1 and q2 are the net charges on the object, and r is the
distance between the two objects.
The distance d between two positively charged particles is Force has an inverse-squared relationship with distance. If the distance is doubled,
measured. The distance between the two particles is then the force will change by a factor of (1/2)^2 = ¼. In other words, the new force
increased to 2d. If the original electrostatic force between will be four times smaller.
the objects was F, what is the new force? Since the two particles are both positive, the force will be a repelling force.
Fe = kq1q2/r2 This constant is called the Coulomb's law constant, and has a value of 9x10^9 N-
m2/C2.
What is the static electric force between a -3.0 μC charge F = kqq/r^2
and a +6 μC charge if they are 2.0 cm apart? F = (9x10^9 N-m2/C2)(3x10^6 C)(6x10^6 C) / (0.02 m)^2
F = 405 N
What if you have more than two charged particles? Sketch the system if a drawing is not provided.
Draw and label a free body diagram.
Calculate all the forces.
Solve for any x and y force components.
Add all the x direction forces together, and then add all the y direction forces
together.
Use the Pythagorean theorem to combine the components into their vector form.
Use arctangent to solve for the direction of the final vector form.
Particle A has a net charge of +4 mC, and is located at F = kqq/r2F
coordinate position (0, 2) m. a on b = (9x109 N-m2/C2)(4x10-3 C)(2x10-3 C) / (2 m)2F
Particle B has a net charge of -2 mC, and is located at a on b = 18,000 N
coordinate position (0, 0) m. F c on b = (9x109 N-m2/C2)(6x10-3 C)(2x10-3 C) / (3 m)2F
Particle C has a net charge of +6 mC, and is located at c on b = 12,000 N
position (3, 0) m. Since these forces don't have any angles, you don't need to solve for their x and y
What is the net charge on particle B? Ignore any gravity components. Solve for the net force and the direction of the net force.
effects. ΣF2 = Fy2 + Fx2
ΣF2 = (18,000 N)2 + (12,000 N)2
ΣF = 21,633 N
tanθ = (18,000 N) / (12,000 N)
θ = tan-1 (1.5)
θ = 56.3°
A neutral pith ball (a small Styrofoam ball) coated with The negatively charged sphere will polarize the pith ball pushing the negative
graphite is suspended between a negatively charged metal charge to the left side of the pith ball. Coulomb's law shows the attractive static
sphere and a neutral metal sphere. The pith ball will force between the negative sphere and the closer positive side of the pith ball will
bounce back and forth between the two metal spheres for be larger than the repelling force between the negative sphere and the further away
a while until it eventually comes to a stop suspended negative side of the pith ball. The pith ball will move into contact with the negative
midway between the two. Explain this behavior. sphere.
Once the pith ball is in physical contact with the metal sphere, negative charge will
conduct onto the pith ball giving the pith ball a net negative charge. The negatively
charged sphere and the negatively charged pith ball will now repel.
The pith ball will repel into the neutral sphere, and will conduct its excess negative
charge onto the neutral sphere. The pith ball will now be neutrally charged, and the
process begins again.
Unless the neutral sphere is grounded, the negative charge between the two metal
spheres will eventually balance, and the pith ball will experience the same static
electric forces from both sides causing it to remain in equilibrium in the middle
between the two.
, Physics 112 Midterm Exam - Questions & Verified Answers
Explain why a charged balloon will electrostatically stick to The balloon will polarize the ceiling. If the balloon is negatively charged, then the
a neutral ceiling. ceiling will polarize such that the positive pole of the ceiling is closer to the balloon
than the negative pole. The attractive static electric force will then be larger than the
repelling static electric force.
As long as the net static force of attraction is equal to or larger than the gravity force
acting on the balloon, the balloon will stick to the ceiling.
Particle A has a net charge of -8.2 μC, and is placed 0.5 m F = kqq/r^2
to the left of Particle B, which has a net charge of +25 nC. F = (9E9 N-m^2/C^2)(8.2E-6 C)(25E-9 C) / (0.5 m)^2
What is the static electric force between the two? F = 7.38E-3 N attractive
Equal. Newton's third law notes that the force of object 1 on object 2 is always equal
b. Which applies the largest force, Particle A on B or but in the opposite direction to the force of object 2 on object 1.
Particle B on A?
Particle A has a net charge of +5.5 μC, and is located at The distance between particles C and A is:
(0,0) m. Particle B has a net charge of -2 μC, and is r2 = 22 + 22
located at (2, 2) m. Particle C has a charge of -2 μC, and is r = 2.83 m
located at (-2, 2) m. What is the net charge on particle A?
Due to symmetry, the force of C on A is the same force as the force of B on A.
F = kqq/r^2
F = (9E9 N-m^2/C^2)(2E-6 C)(5.5-6 C) / (2.83 m)^2
F = 0.0124 N
The x components of the forces cancel out so the net force will be equal to the sum
of the two y-component forces.
ΣF = ΣFy = (0.0124 N)(sin 45) + (0.0124 N)(sin 45)
ΣF = 0.0175 N at 90°
Particles A and B both have a net charge of +q, and are a. F is proportional to the inverse square of distance.
separated by distance d. Explain how each of the following 1/32 = 1/9 F
changes will affect the static electric force Fe. The force will decrease by a factor of 9.
a. The distance between the two is increased to 3d b. F is proportional to q.
The force will double or 2F.
b. The charge on particle A is increased to +2q
c. F and q are directly proportional, so an x3 increase in q will result in an x3
c. The charge on particle B is increased to +3q and the increase in F.
distance is decreased to 1/3 d F and r have an inverse square relationship, so a 1/3 change in r will result in an x9
increase in F.
Combined, this means that F will increase by a factor of 3 x 9 = x27 above the
original
system force.
Two charged particles have opposite net charges. They The particles will accelerate towards each other with an increasing acceleration.
are placed near each other, and released from rest. Which
of the following statements best describes the motion of
the particles? Since the charges are opposite, they will attract, and move towards each other.
Since the static electric force between the two will increase as the particles get
closer together, the acceleration will also increase according to Newton's second
law (ΣF = ma).
What is the net charge on an object that has gained 8 x (810^13)(-1.610^-19)= -1.28*10^-5 Coulombs.
10^13 electrons?
-1.3 x 10-5 C
A particle with a net charge of -2 μC is halfway between kqq/r^2 - kqq/r^2
two particles with a net charge of +4 μC and +6 μC, (9x10^9)(2x10^-6)(4x10^-6)/(0.05)^2=28.8
respectively. The two positively charged particles are 10 (9x10^9)(2x10^-6)(6x10^-6)/(0.05)^2=43.2
cm apart. What is the magnitude of the net force on the 43.2-28.8=
negative particle?
14.4 N
Which of the following statements regarding charge is All of the above are accurate.
most accurate?
If two objects both have more of the positive type of charge then the objects will repel each other.
than negative (usually referred to as a positive net charge)
If two objects both have more of the negative type of then the objects will repel each other.
charge than positive (referred to as a negative net charge)
If one object has more of the positive type of charge and then the objects will attract each other.
one object has more of the negative type of charge
If a material gains electrons the material will have a negative net charge
If a material loses electrons the material will have a positive net charge.
A particular object has a net 6.5 μC of the positive type of Since the object has extra of the positive type of charge, electrons must have been
charge. Were electrons transferred onto or off the object? transferred off the material. Since electrons carry the negative type of charge,
How many? removing electrons would have left behind more positive than negative.
The total amount of charge moved off the material was 6.5 μC. Each electron
moved off carries 1.6x10-19 C. Convert μC into C and divide.
6.5x10-6 C / 1.6x10-19 C = 4.06x1013 electrons were removed.
Solve for the number of charge carrier particles (protons or The amount of charge carried by one electron is 1.6x10-19 C. Divide the total
electrons) transferred on or off the object. charge by the charge of one electron to solve for the number of electrons.
(3.5x10-6 C) / (1.6x10-19 C) = 2.25x1013 electrons were transferred off the object.
conductors Materials that allow electrons to move easily through them. Metals are good
conductors
insulators Materials that do not allow electrons to move freely through them. Nonmetals are
good insulators
Semiconductors are a class of materials that, as you might expect, share properties of both.
Conduction is the movement of charge from one object to another. It is easy to move charge
from metal to metal (conductor to conductor) but much more difficult to move charge
from insulator to insulator.
The transfer of charge caused by rubbing two objects against each other is a
special type of conduction called triboelectric charging.
An electroscope is a device that has small gold foil strips The negative charge on the rod repels the negative charge already present in the
suspended from a metal rod. If a negatively charged rod is electroscope. Since the electroscope is made from metals, electrons will be pushed
brought near the top of a neutral electroscope, the gold foil down into the gold strips. The electroscope is now polarized (the top is more
strips will separate. (See below.) Explain why this positive, and the bottom is more negative). However, the relocated negative charge
happens. now in the thin gold strips will repel each other causing the gold strips to separate.
Induction is a charge transfer process that involves polarizing an object and then allowing
charge to transfer to another object through conduction. While still under the
influence of the dipole, the charge transfer mechanism is removed (the two objects
are moved apart). The two objects are now charged.
, Physics 112 Midterm Exam - Questions & Verified Answers
Polarization is a redistribution of charge rather than a transfer of charge; the total amount of
charge on the polarized object does not change.
static electric force Proportional to the quantity of net charge on both objects, and proportional to the
inverse-square of the distance between the two charged objects.
In other words:
Fe α q1q2 / r2
Where Fe is the force, q1 and q2 are the net charges on the object, and r is the
distance between the two objects.
The distance d between two positively charged particles is Force has an inverse-squared relationship with distance. If the distance is doubled,
measured. The distance between the two particles is then the force will change by a factor of (1/2)^2 = ¼. In other words, the new force
increased to 2d. If the original electrostatic force between will be four times smaller.
the objects was F, what is the new force? Since the two particles are both positive, the force will be a repelling force.
Fe = kq1q2/r2 This constant is called the Coulomb's law constant, and has a value of 9x10^9 N-
m2/C2.
What is the static electric force between a -3.0 μC charge F = kqq/r^2
and a +6 μC charge if they are 2.0 cm apart? F = (9x10^9 N-m2/C2)(3x10^6 C)(6x10^6 C) / (0.02 m)^2
F = 405 N
What if you have more than two charged particles? Sketch the system if a drawing is not provided.
Draw and label a free body diagram.
Calculate all the forces.
Solve for any x and y force components.
Add all the x direction forces together, and then add all the y direction forces
together.
Use the Pythagorean theorem to combine the components into their vector form.
Use arctangent to solve for the direction of the final vector form.
Particle A has a net charge of +4 mC, and is located at F = kqq/r2F
coordinate position (0, 2) m. a on b = (9x109 N-m2/C2)(4x10-3 C)(2x10-3 C) / (2 m)2F
Particle B has a net charge of -2 mC, and is located at a on b = 18,000 N
coordinate position (0, 0) m. F c on b = (9x109 N-m2/C2)(6x10-3 C)(2x10-3 C) / (3 m)2F
Particle C has a net charge of +6 mC, and is located at c on b = 12,000 N
position (3, 0) m. Since these forces don't have any angles, you don't need to solve for their x and y
What is the net charge on particle B? Ignore any gravity components. Solve for the net force and the direction of the net force.
effects. ΣF2 = Fy2 + Fx2
ΣF2 = (18,000 N)2 + (12,000 N)2
ΣF = 21,633 N
tanθ = (18,000 N) / (12,000 N)
θ = tan-1 (1.5)
θ = 56.3°
A neutral pith ball (a small Styrofoam ball) coated with The negatively charged sphere will polarize the pith ball pushing the negative
graphite is suspended between a negatively charged metal charge to the left side of the pith ball. Coulomb's law shows the attractive static
sphere and a neutral metal sphere. The pith ball will force between the negative sphere and the closer positive side of the pith ball will
bounce back and forth between the two metal spheres for be larger than the repelling force between the negative sphere and the further away
a while until it eventually comes to a stop suspended negative side of the pith ball. The pith ball will move into contact with the negative
midway between the two. Explain this behavior. sphere.
Once the pith ball is in physical contact with the metal sphere, negative charge will
conduct onto the pith ball giving the pith ball a net negative charge. The negatively
charged sphere and the negatively charged pith ball will now repel.
The pith ball will repel into the neutral sphere, and will conduct its excess negative
charge onto the neutral sphere. The pith ball will now be neutrally charged, and the
process begins again.
Unless the neutral sphere is grounded, the negative charge between the two metal
spheres will eventually balance, and the pith ball will experience the same static
electric forces from both sides causing it to remain in equilibrium in the middle
between the two.
, Physics 112 Midterm Exam - Questions & Verified Answers
Explain why a charged balloon will electrostatically stick to The balloon will polarize the ceiling. If the balloon is negatively charged, then the
a neutral ceiling. ceiling will polarize such that the positive pole of the ceiling is closer to the balloon
than the negative pole. The attractive static electric force will then be larger than the
repelling static electric force.
As long as the net static force of attraction is equal to or larger than the gravity force
acting on the balloon, the balloon will stick to the ceiling.
Particle A has a net charge of -8.2 μC, and is placed 0.5 m F = kqq/r^2
to the left of Particle B, which has a net charge of +25 nC. F = (9E9 N-m^2/C^2)(8.2E-6 C)(25E-9 C) / (0.5 m)^2
What is the static electric force between the two? F = 7.38E-3 N attractive
Equal. Newton's third law notes that the force of object 1 on object 2 is always equal
b. Which applies the largest force, Particle A on B or but in the opposite direction to the force of object 2 on object 1.
Particle B on A?
Particle A has a net charge of +5.5 μC, and is located at The distance between particles C and A is:
(0,0) m. Particle B has a net charge of -2 μC, and is r2 = 22 + 22
located at (2, 2) m. Particle C has a charge of -2 μC, and is r = 2.83 m
located at (-2, 2) m. What is the net charge on particle A?
Due to symmetry, the force of C on A is the same force as the force of B on A.
F = kqq/r^2
F = (9E9 N-m^2/C^2)(2E-6 C)(5.5-6 C) / (2.83 m)^2
F = 0.0124 N
The x components of the forces cancel out so the net force will be equal to the sum
of the two y-component forces.
ΣF = ΣFy = (0.0124 N)(sin 45) + (0.0124 N)(sin 45)
ΣF = 0.0175 N at 90°
Particles A and B both have a net charge of +q, and are a. F is proportional to the inverse square of distance.
separated by distance d. Explain how each of the following 1/32 = 1/9 F
changes will affect the static electric force Fe. The force will decrease by a factor of 9.
a. The distance between the two is increased to 3d b. F is proportional to q.
The force will double or 2F.
b. The charge on particle A is increased to +2q
c. F and q are directly proportional, so an x3 increase in q will result in an x3
c. The charge on particle B is increased to +3q and the increase in F.
distance is decreased to 1/3 d F and r have an inverse square relationship, so a 1/3 change in r will result in an x9
increase in F.
Combined, this means that F will increase by a factor of 3 x 9 = x27 above the
original
system force.
Two charged particles have opposite net charges. They The particles will accelerate towards each other with an increasing acceleration.
are placed near each other, and released from rest. Which
of the following statements best describes the motion of
the particles? Since the charges are opposite, they will attract, and move towards each other.
Since the static electric force between the two will increase as the particles get
closer together, the acceleration will also increase according to Newton's second
law (ΣF = ma).
What is the net charge on an object that has gained 8 x (810^13)(-1.610^-19)= -1.28*10^-5 Coulombs.
10^13 electrons?
-1.3 x 10-5 C
A particle with a net charge of -2 μC is halfway between kqq/r^2 - kqq/r^2
two particles with a net charge of +4 μC and +6 μC, (9x10^9)(2x10^-6)(4x10^-6)/(0.05)^2=28.8
respectively. The two positively charged particles are 10 (9x10^9)(2x10^-6)(6x10^-6)/(0.05)^2=43.2
cm apart. What is the magnitude of the net force on the 43.2-28.8=
negative particle?
14.4 N
Which of the following statements regarding charge is All of the above are accurate.
most accurate?
