E & M UNIT 2 – Objectives
EM II - Objectives
By the time you finish all labs, worksheets and related activities, you should be able to:
1 Draw parallels between gravitational and electrical: force, field, energy & potential.
Write formulas for each expression.
Solve for units for each quantity.
2. Map equipotential lines, explain their significance in terms of the field.
3. Use the volt as the unit of electric potential; use two different equations for potential.
4. Explain how a capacitor works.
5. Relate capacitance to plate area and separation.
6. Relate energy storage by a capacitor to charge and potential
7. Use relationships among potential, field, charge and energy to solve for missing quantities.
Review
1. Whether it be gravitational or electrical, an object with “stuff” (mass or charge) experiences a constant force in a uniform field.
Gravitational
[pic] [pic] [pic]
It requires work (transfer of energy) to raise an object with mass against the gravitational field.
Electrical
[pic] [pic] [pic]
It requires work to move a test charge against the electric field.
2. An object that “falls” in a field will accelerate as potential energy is transferred to kinetic energy.
[pic]
3. Electric equipotentials around distributions of charge are like contour lines on a topographic map.
Moving from A to B does not cost any energy because both points are at the same potential.
If the potential difference between the charges is 6.0 V, then moving a proton from B to C would cost you 3.0 eV or 4.8 x 10-19 J of energy.
By contrast, an electron would lose that much potential energy as it moved to a position closer to the (+) charge.
4. Electric equipotentials between charged plates are parallel to the plates; the potential changes uniformly as one moves from one plate to the other.
As before, it does not cost you energy to move a charged particle from B to A.
However, if the potential difference between the plates were 12.0 V, then moving a proton from B to C would cost you 6.0 eV or 9.6 x 10-19 J.
5. Moving charge from one plate of a capacitor to another requires a source of energy (Genecon or battery).
Connecting a battery providing a potential difference of ∆V to the capacitor will cause a quantity of charge, q, to move from one plate to the other. Charge stops moving when the potential difference between the plates matches that of the battery. At that point,the battery can no longer force charge to flow.
If the potential difference applied to the plates were doubled, then twice as much charge would be moved from one plate to the other. The energy stored in the capacitor is 4x as great as before because both charge and potential are doubled.
The capacitance, C. is the slope of the q vs V graph. Capacitor 1 has a greater capacitance than does capacitor 2. The equation of the line is [pic].
[pic]
6. The energy stored in a capacitor is the average of the energy of each charge that is moved from one plate to the other. It is given by [pic] or [pic].
The 1/2 factor takes into account that the potential difference between the capacitor plates decreases as the capacitor is discharged. The average potential difference is 1/2 way between 0 and the maximum value.
7. The capacitance, C, is directly proportional to the area of the plates and is inversely proportional to the distance between them. [pic].
It is worthwhile to play “What would happen if…” games with this relationship. For example, doubling the area, while keeping V constant, allows twice as much charge to move between the plates; thus C is doubled. Similarly, doubling d while the capacitor is still connected to the battery (V is constant), reduces the amount of charge on the plates to 1/2 its original value; thus the capacitance is halved.
What would change if d were doubled after the battery was disconnected (so q remains constant)?
EM II: Worksheet 1
Fields, Potential, and Energy
1. Two books, initially on the floor, are picked up and placed on a shelf 2.0 m off the floor. One, Twenty Other Things I Like To Do With That Stuff Between My Toes, has a mass of 1.0 kg. The other, Why Physics Rules The Universe, has a mass of 2.0 kg. The gravitational field strength near the surface of the Earth is approximately 10 N/kg.
a. Calculate the gravitational force acting on each book as it rests on the shelf. What factors determine the size of this force?
b. Calculate the change in each book’s gravitational potential energy as a result of being picked up off the floor and placed on the shelf. What factors determine the size of this change?
c. What is the difference in gravitational potential (potential energy per unit mass) between the floor and the shelf (use data from each book to calculate this)? What factors determine the size of this difference?
d. How does gravitational potential differ from gravitational potential energy?
2. Below are two parallel conducting plates, each carrying an equal quantity of excess charge of opposite type. The plates are separated by 2.0 m.
Between the pair of plates are two positively charged objects; the object on the left carries 1.0 µC of excess charge, the object on the right carries 2.0 µC. The electric field strength between the plates is uniform, and approximately 10 N/C. You move each charge from the negative plate to the positive plate. [for this example, neglect the effects of the gravitational field]
a. Calculate the electrical force acting on each object when it is between the plates. What factors determine the size of this force?
b. Calculate the change in each object’s electrical potential energy as a result of being moved from the negative plate to the positive plate. What factors determine the size of this change?
c. What is the difference in electric potential (potential energy per unit charge) between each of pairs of plates? What factors determine the size of this difference?
d. What is the difference in electric potential between the negative plate and a point midway between the plates?
e. How does electrical potential differ from electric potential energy?
3. In unit 1, the units for electric field were given as [pic]. It turns out that the electric field strength can also be given in [pic]. Show how these units, which appear very different, actually describe the same quantity.
EM II - Worksheet 3
Electric Potential Energy
For each problem below, identify which situation (final or initial) has more electrical potential energy. Explain your reasoning.
1. Initial Final Explanation
[pic]
2. Initial Final Explanation
[pic]
3. Initial Final Explanation
[pic]
4. A hydrogen atom has a negatively charged electron that occupies the space around the positively charged proton at its nucleus. The figure below shows this. The electron makes a circular orbit around the proton.
Initial Final Explanation
[pic]
5. This figure shows a different hydrogen atom.
Initial Final Explanation
[pic]
6. Given the three charges below, compare the energy of the initial and final states.
Initial Final Explanation
[pic]
7. Given the three charges below, compare the energy of the initial and final states.
Initial Final Explanation
[pic]
8. In the space below, make up your own arrangement of three charged particles and compare the electric potential energies as you did in #6 and #7.
Initial Final Explanation
9. A cart on a track has a large, positive charge on the top and is located between two sheets of charge. Initially at rest at point A, the cart moves from A to C.
a. Draw qualitative force diagrams for the cart when it is at each position A, B and C.
b. Draw qualitative energy bar charts for the cart when it is at each position A, B and C.
(Be sure to first identify the objects that make up your system.)
10. How would your force and energy diagrams change (if at all) if the sheet to the right were also positively charged?
EM III: WORKSHEET 3a
To Accompany "EM Field" Software
(See the worksheet on Field for suggestions on how to use the EM program.)
Exploring potential around a point charge
Place a positive "8" charge in the middle of your screen. From the "Field and Potential" menu, select "Potential."
1. Click your pointer around the charge.
a) What do you notice about the value of potential as you move away from the charge?
b) Why is only a value given for potential? Why isn’t a directional arrow given as well?
2. Release the mouse: this will leave a potential value on the screen.
a) How can you create four identical values? Test your prediction.
b) What relationship might exist between potential and distance from the point charge? Test your prediction.
c) Erase the potential values. Go now to the "Field and Potential" menu and select "Equipotential lines." Click on the screen around the charge to create lines which represent positions of equal potential.
i - Why are all the lines circular?
ii - Where is the line representing 0.0 volts?
3. Erase the equipotential lines and replace the positive charge with a negative "8" charge.
a) Compared to the situation with the positive charge, how will the potential values around the negative charge:
i - be the same?
ii - be different?
To test your prediction, you will have to go back to the "Field and Potential" menu and select "Potential".
b) How are lines of equal potential around the negative charge different from those around a positive charge? Where is the line of representing 0.0 volts around a negative charge?
4. Erase markings on the screens. Place a positive "4" and a negative "4" charge on the screen about 8 centimeters apart.
a) Use the "Potential" values option to determine what the potential is around the two charges . After completing your exploration, answer the following questions:
i - In what place or places is the largest positive value of potential found?
ii - In what place or places is the largest negative value of potential found?
iii - Where is the potential zero?
iv - Describe as best you can the general pattern of potential values.
b) Draw lines below representing places of equal potential: you should draw four or five such lines, including the line representing places where the potential is 0 volts. If you like, use the "Equipotential" option in the program to help you complete your diagram.
[pic]
i - Looking at the diagram you have just created, would energy be required to move a positive charge from point A to point B? from point B to point A? Why or why not?
ii - On your diagram above, make a heavy line representing the path along which a negative charge could be move without losing or gaining potential energy; mark this line “Energy Free Path.”
5. Erase all markings. Leaving the positive "4" charge in place, replace the negative "4" charge with a second positive "4" charge.
a) Use the "Potential" values option to determine what the potential is around the two charges . After completing your exploration, answer the following questions:
i - Where else is the value of potential 0 volts?
ii - If you placed a small positive charge halfway between the two positive "4" charges, how would it move?
Would the potential of this small positive charge at this halfway point be more than, less than, or equal to 0volts?
iii - Describe as best you can the general pattern of potential values.
iv - Is work needed to move a small positive charge towards the positive charges? Why or why not?
v - Is work needed to move a small negative charge towards the positive charges? Why or why not?
b. Draw below the shape of the electric field. If you like, use the "Field Line" option in the program to help you complete your diagram.
[pic]
Exploring potential between parallel plates
As we did when exploring electric field around parallel plates, create a "plate" of charge by placing at least ten positive "4" charges in a line, each charge making contact with the charge next to it. Make a second line of an equal number of negative "4" charges parallel to the line of positive charge and about 5 cm away from it.
Select "Equipotential Lines" from the "Field and Potential" menu and determine where the lines of equal potential lie between the two plates. Make a diagram of your results below:
[pic]
Answer these questions based upon your explorations:
a) As you move from the middle of the positive line of charge to the middle of the negative line of charge, how does the potential vary?
Did the electric field strength vary in the same or in a different way? Explain briefly.
b) Suppose you placed a small positive charge close to the positive line of charge (for example, at point "Z" on the diagram).
i - Describe the change in potential energy as the charge moves.
ii - Describe the change in kinetic energy as the charge moves.
EM III - Worksheet 4
1. An electron is placed midway between two parallel conducting plates that are spaced 3.0 mm apart. The plates are attached to the terminals of a 12.0 V battery.
[pic]
a. What is the direction and magnitude of the electric field?
b. How much work would be done by moving the electron from the midpoint to the surface of the (-) plate?
Express in both J and eV.
c. If the electron were released from a point midway between the plates, what would be its velocity when it struck the (+) plate?
d. If the potential difference were doubled, how much faster would the velocity be?
2. Robert Millikan determined the charge of an electron by suspending a charged drop of oil between two parallel plates like those shown at right.
a. What forces act on the suspended oil drop? Draw a force diagram that supports your answer.
b. Assuming the mass of the oil drop is 4.0 x 10-15 kg , the potential difference between the plates is 1630 V, and the separation between the plates is 0.020 m, what is the charge on the oil drop?
c. How many excess electrons are on the oil drop?
3. A beam of protons is shot with an initial velocity of 5.00 x 106 m/s at a metal plate. This plate has a potential 4.00 kV higher than the proton beam source. What is the velocity of the protons just prior to striking the plate?
4. An unknown charged particle (an electron or proton) is placed at point A between two parallel plates. The particle is released from rest and accelerates toward the other plate. The particle emerges through the hole at point B with a speed of 1.4 x 105 m/s. The potential difference between the two plates is 100V.
a. Is the unknown particle an electron or proton? Justify your answer.
b. Which plate (top or bottom) is positively charged?
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