Lesson 9: Electricity
A Test Charge (2.5⋅10^-16 C) is placed 2.4 meters from a Source Charge (7.8⋅10^-13 C). What is the strength of the Electric Field? (A) 7.89⋅10^-2 N/C (B) 3.22⋅10^-2 N/C (C) 6.75⋅10^-3 N/C (D) 1.22⋅10^-3 N/C
(D) 1.22⋅10^-3 N/m E = k (Q / r^2) E = (9⋅10^9)((7.8⋅10^-13) / (2.4^2)) E = (9⋅10^9)(approx. 1.5⋅10^-13 (actual: 1.35⋅10^-13)) E = approx. 1⋅10^-3 N/C (actual: 1.215⋅10^-3)
In ______________, the positively charged nucleus cannot move around. In ______________, the negatively charged electrons cannot move around. (A) insulators, insulators (B) insulators, insulators and conductors (C) insulators and conductors, insulators and conductors (D) insulators and conductors, insulators
(D) insulators and conductors, insulators In insulators and conductors, the positively charged nucleus cannot move around. In insulators, the negatively charged electrons cannot move around. Recall conductors and electrons freely moving from valence
Like Charges __________ and Opposite Charges __________. (A) attract, attract (B) attract, repel (C) repel, repel (D) repel, attract
(D) repel, attract Like Charges repel and Opposite Charges attract.
What is the value of 1 coulomb in relation to e (fundamental unit of charge)
1C= 6.24 * 10^18 e
A "Ground" is an infinite reservoir for electrons. What does that mean? Give an example.
A "Ground" is an infinite reservoir for electrons, which means that it can accept an infinite number of electrons. An example would be the earth.
*CRB* Compare the composition and effects of Conductors and Insulators.
Conductors have those free Conduction Electrons that can move in response to an electric field. A good conductor will have many ions dissolved, or a metal with a Sea of Electrons. Insulators have no free charges, but rather the electrons are tightly held, restricting any flow of electrons.
True or False. It is possible for a certain particle with a charge of +9 C to split into two smaller particles with charges of +3 C and +5 C as long as 1 C of charge is converted into heat.
False. According to the Law of Conservation of Charge. Charge will always be conserved. You may not always have the same individual magnitudes of charge but the total charge will remain the same
What is the units for volts?
Joules/Coulomb So electric potential is in volts
The closer a similarly charged Test Charge is to a Source Charge, the higher or lower the Electric Potential? Why?
The closer the Test Charge is to the Source Charge, the higher the Electric Potential. This is because the charges will move away from each other (essentially decreasing their potential for generating kinetic energy from their Electric Potential).
How is the strength of an electric field depicted in a diagram with electric field lines?
The more lines in a given area, the stronger the electric field is implied to be.
*CRB* True or false? Because the increasing distance between charged particles repelling each other will decrease the Electrostatic Force, they will also slow down as they move.
True. Because the increasing distance between charged particles repelling each other will decrease the Electrostatic Force, they will also decelerate (not accelerate in the opposite direction!).
What equation is used to relate Electric Potential (V) to the Source Charge (Q)?
V = k (Q / r) V = Electric Potential k = Coulomb's Constant (9⋅10^9) Q = Source Charge r = Radius between Q and q
Give a real life example of the Triboelectric Effect.
When you rub your feet on a carpet and charge builds up on your body.
Why is the charge of an electron considered the "Fundamental Unit of Charge"?
You cannot divide an electron and therefore the charge of an electron is the smallest possible unit of charge; thus, we refer to it as the "Fundamental Unit of Charge". In other words, that charge is quantized. Electron has same but opposite charge as proton
*CRB* Knowing that F = q x E, use Newton's Second Law to find the acceleration caused by the charge in the electric field.
a = F / m = q x E / m a = acceleration (m/s^2) F = Force (N) q = Charge (C) m = Mass (kg)
*CRB* In that previous example, if you had doubled the distance between the two charges, how would their Electrostatic Force changed? (A) It would have quadrupled (B) It would have doubled (C) It would be halved (D) It would be quartered
(D) It would be quartered There is an inverse squared relationship, since r^2 is in the denominator of the equation.
q1 (3.4⋅10^-14 Coulombs) and q2 (2.1⋅10^-9 Coulombs) are exactly 3.2⋅10^-3 m apart. What is the value of the Electrostatic Force (in N) between these two charges (k = 9⋅10^9)? (A) 6.27⋅10^-8 (B) 3.24⋅10^-9 (C) 9.66⋅10^-20 (D) 7.32⋅10^-21
(A) 6.27⋅10^-8 Fe = k ((q1q2) / r^2) Fe = (9⋅10^9)⋅(((3.4⋅10^-14)(2.1⋅10^-9)) / (3.2⋅10^-3)^2) Fe = (9⋅10^9)⋅(((approx. 7⋅10^-23 (actual: 7.14⋅10^-23))) / (3.2⋅10^-3)^2) Fe = (9⋅10^9)⋅(((approx. 7⋅10^-23 (actual: 7.14⋅10^-23))) / approx 1⋅10^-5 (actual 1.02⋅10^-5)) Fe = (9⋅10^9)⋅(approx. 7⋅10^-18 (actual: 6.97⋅10^-18)) Fe = approx. 6⋅10^-8 N (actual: 6.27⋅10^-8)
*CRB* A Dielectric is a substance that is normally not polarized, but in an electric field, a small charge can be induced. This acts to stabilize the source charge, and can allow more charges to be stored. Which of the following could be a dielectric? (A) Insulator (B) Conductor (C) Neither Insulator nor Conductor (D) Both Insulator and Conductor
(A) Insulator An Insulator is a Dielectric that is normally not polarized, but in an electric field, a small charge can be induced. This acts to stabilize the source charge, and can allow more charges to be stored.
A Test Charge (2.5⋅10^-16 C) is nearby a Source Charge (7.8⋅10^-13 C). If the Fe is equal to 45.7 N, what is the strength of the Electric Field? (A) 7.65⋅10^-15 N/C (B) 1.83⋅10^17 N/C (C) 4.43⋅10^-17 N/C (D) 9.32⋅10^18 N/C
(B) 1.87⋅10^17 C/m Fe / q = E E = 45.7 / 2.5⋅10^-16 E = approx. 2⋅10^17 N/C (actual: 1.83⋅10^17)
*CRB* Fill in the blanks: Positively charged particles will tend to move towards ___________ potential, whereas negatively charged particles will tend to move towards _________ potential. (A) Higher, Lower (B) Lower, Higher (C) Positive, 0 (D) 0 , Negative
(B) Lower, Higher Positively charged particles will tend to move towards Lower potential, whereas negatively charged particles will tend to move towards Higher potential.
Electric Field Lines are drawn in the direction that a _________ Test Charge would move. (A) neutral (B) positive (C) negative (D) energized
(B) positive Electric Field Lines are drawn in the direction that a positive Test Charge would move. So if the source charge is positive, the electric field lines would be drawn going outwards
*CRB* We have looked at the effects of two charges acting on each other so far, in real life, multiple charges will all have electrostatic interactions. According to the Principle of Superposition, how would you determine the Net Electric Force on a single charge? (A) By adding the magnitudes of charges and finding the most common direction. (B) By adding the magnitudes of charges only. (C) By adding the vectors of individual electrostatic interactions together. (D) By subtracting the vectors of individual electrostatic interactions.
(C) By adding the vectors of individual electrostatic interactions together.
A Test Charge (6.7⋅10^-14 C) is sitting 2.4⋅10^-3 meters away from a Source Charge (4.2⋅10^-12 C). What is the Electric Potential Energy (in J) between these two charges? (A) 4.55⋅10^-9 (B) 6.87⋅10^-10 (C) 2.23⋅10^-11 (D) 1.05⋅10^-12
(D) 1.05⋅10^-12 V = k (Q / r) V = (9⋅10^9) ((4.2⋅10^-12) / (2.4⋅10^-3)) V = (9⋅10^9) (approx. 2⋅10^-9 (actual: 1.75⋅10^-9)) V = approx. 18 (actual: 15.75) EPE / q = V EPE / 6.7⋅10^-14 = 18 EPE = 1⋅10^-12 J (actual: 1.05⋅10^-12) *Need help with MCAT math? Become an MCAT math wizard using Andrew's High-speed Math Mastery Course @ https://mcatselfprep.com/course/andrews-high-speed-math-mastery-course/*
A Test Charge (6.7⋅10^-14 C) is sitting 2.4⋅10^-3 meters away from a Source Charge. What is the Electrostatic Force (in N) between these two charges if the Voltage is equal to 4.3 V at that point? (A) 9.87⋅10^-12 (B) 4.32⋅10^-15 (C) 2.88⋅10^-13 (D) 1.20⋅10^-10
(D) 1.20⋅10^-10 EPE / q = V EPE / (6.7⋅10^-14) = 4.3 EPE = (6.7⋅10^-14) x (4.3) EPE = approx. 3⋅10^-13 J (actual: 2.881⋅10^-13) Fe = EPE / r Fe = (3⋅10^-13) / (2.4⋅10^-3) Fe = approx. 1⋅10^-10 N (actual: 1.20⋅10^-10) *Need help with MCAT math? Become an MCAT math wizard using Andrew's High-speed Math Mastery Course @ https://mcatselfprep.com/course/andrews-high-speed-math-mastery-course/*
*CRB* What is this Fundamental Unit of Charge equal to, in Coulombs? (A) 1 (B) 9 x 10^9 (C) 6.636 x 10^-34 (D) 1.6 x 10^-19
(D) 1.6 x 10^-19 Coulombs
Electrons and protons have ____________ absolute value of charge and __________ mass. (A) different, different (B) different, the same (C) the same, the same (D) the same, different
(D) the same, different Electrons and protons have the same absolute value of charge and different mass.
What equation can be used to relate E to the distance between two charges?
E = k (Q / r^2) E = Electric Field Strength Q = Source Charge r = Distance between Q and q
What equation can be used to relate Electric Potential Energy to Electric Potential?
EPE / q = V EPE = Electric Potential Energy q = Charge V = Electric Potential
What is the difference between Electric Potential and Electric Potential Energy?
Electric Potential Energy is the amount of energy required to move a charge from one location to another (units = J). Amount of work you need to apply to take a particle from one spot to another. Electric Potential is the amount of energy required to move a charge from one location to another per unit charge (units = J/C). How much work is necessary per unit of charge.
In an electric field with a field strength of 5 N/C, how much work does it take to take a positively charged (2 coulomb) charge, 3 meters toward the positive plate in the field?
Electric field is force per charge, so the force of the field exerted on the 2 coulomb charge in its present location is 10 N. SO we need a little more than 10 Newtons of force exerted towards the positive plate. Work is = 10N * 3m= 30 J So potential energy of charge at the new location relative to where it started is 30 J Overall electrical potential energy and gravitational potential energy is not really that much different, just the source of field is different.
True or False? A charge is repelled from another charge. As the two charges get farther away from one another, they will move slower and slower.
False. A charge is repelled from another charge. As the two charges get farther away from one another, they will *accelerate* at a slower and slower rate due to the decreasing Electrostatic Force. Remember that Force is not directly related to velocity but rather acceleration.
What equation can be used to relate Electric Field Strength (E) to Electrostatic Force (Fe)
Fe / q = E Fe = Electrostatic Force q = Test Charge E = Electric Field Strength
What equation can be used to relate Electrostatic Force to Electric Potential Energy?
Fe = EPE/r (similar to F = mgh) Fe = Electrostatic Force EPE = Electric Potential Energy r = Radius between the two charges
Coulomb's Law can be used to quantify the force between two charges. Write out this equation.
Fe = k ((q1q2) / r^2) Fe = Electrostatic Force k = Coulomb's Constant (9⋅10^9) q1 = Charge 1 q2 = Charge 2 r = Radius between q1 and q2
Compare the process of Charge by Conduction to Charge by Induction.
In Charge by Conduction, you charge a neutral object by physically touching a negatively-charged object to it. In Charge by Induction a charge is induced by bringing a negatively charged object close to another object.
If you add for example, extra negative charge to insulators, what will happen? What about conductors?
In insulators, remember the charges cannot move, so they will stay wherever they were inserted. In conductors, the charges are able to move and since like charges repel, they will try to get as far away as they can from each other and move towards the outer edge of the conductor. NOTE: to make either of these more positive, instead of adding a positive charge, you remove a negative charge.
Illustrate how induction using a Ground could result in a neutral metal ball becoming negatively charged.
Induction initially shifts the location of charges in molecule, and because it is attached to a ground, the like charges will leave the ball making the once neutral ball charged. Note that the wire is cut in between steps b and c so that the escaped charges can't come back
You put a negatively-charged balloon on a wall. If the wall is an insulator, then why does the balloon stick to the wall?
Insulators can still polarize temporarily. The electrons move slightly further from the balloon while the protons move slightly closer to the balloon, resulting in a partial-positive charge near the balloon. The actual atom won't move but the nucleus will shift its position slightly making one side of the atom distinctly positive and the other distinctly negative.
What is the units for Ke in coloumbs law?
Ke= (Nm^2)/c^2
*CRB* You make a physicist friend who offers to tutor you in physics for the MCAT. He says his research is about to earn him a huge grant, since he recently found a novel molecule with a charge of -4.2 x 10^-19 Coulombs. Should you hire this tutor?
Since this physicist's charged molecule has a charge that shouldn't be possible according to the Fundamental Unit of Charge, you probably shouldn't hire this tutor! This charge is well bellow the fundamental unit of charge which is the lowest possible charge
Compare Source Charge (Q) and Test Charge (q).
The Source Charge (Q) is the charge that is generating the Electric Field. The Test Charge (q) is the charge that is being used to determine the strength and direction of the Electric Field.
*CRB* Describe the Triboelectric Effect/Triboelectric Charging.
Triboelectric Charging is a form of contact electrification, where two different materials will charge each other after coming into frictional contact. Such as rubbing a balloon on your head causing an attractive force
*CRB* True or false? Because Electric Potential is dividing work by charge, positively and negatively charged particles will move naturally towards different potentials.
True. Because Electric Potential is dividing work by charge, positively and negatively charged particles will move naturally towards different potentials.
*CRB* True or false? Even if there are no other charges to affect, a single charge (the source charge) will still create an electric field.
True. Even if there are no other charges to affect, a single charge (the source charge) will still create an electric field.
True or False? It is possible for a certain particle with a charge of 0 C to split into two smaller particles with charges of +3 C and -3 C.
True. It is possible for a certain particle with a charge of 0 C to split into two smaller particles with charges of +3 C and -3 C. The overall charge was preserved.
Electric potential formula:
V=K (Q/ D) K= 9 *10^9 Nm^2/c^2 Q = charge creating the electric potential D= distance between charge creating the V and the point where you want the v value at. Notice the Yellow voltage measurement in pic
What's the difference between Electric Potential and Voltage?
Voltage (ΔV) refers to a difference in Electric Potential (V) between two points.
You rub a balloon against your head and then hold it near your head. Considering that the balloon became negatively charged, what about your hair makes it attracted to the balloon, causing it to stand up?
When the balloon is brought close to your head, the negatively-charged balloon repels the electrons in your hair, sending them down closer to your head, making the ends of your hair positively-charged, resulting in its attraction to the balloon. Note that when you rub balloon on head, it is grabbing electrons from your hair making the balloon negatively charged