Honors Assignment – Electrostatics
Reading Chapter Sections: 16: 1 – 9; 17: 1 – 5, 7
Objectives/HW
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The student will be able to: |
HW: |
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1 |
Relate electrical phenomena to the motion and position of the fundamental charge found on electrons and protons and recognize the Coulomb as the SI unit of charge and e as the elementary quantum of charge. |
1 – 8 |
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2 |
State and apply Coulomb’s Law to solve problems relating force, charge, and distance. |
9 – 15 |
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3 |
Define and apply the concept of an electric field and sketch field lines for a given distribution of charge and solve for the electric field strength at any point relative to a collection of point charges. |
16 – 20 |
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4 |
Define electric potential and potential difference and the Volt and solve problems relating electric potential to charge, work or energy, electric field strength and distance. |
21 – 28 |
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5 |
Define capacitance and the Farad and solve related problems, including analysis of energy stored in a capacitor. |
29 – 31 |
Homework Problems
1. If you comb your hair on a dry day, your hair may stand on end indicating that it has become electrically charged. Can the comb that you used remain electrically neutral? Explain.
2. As you walk across a rug electrons may be removed from your shoes and deposited in the rug. Does the rug become positively or negatively charged? What about your shoes?
3. A positively charged rod is brought near a neutral pith ball that is hanging from an insulating string. At first the pith ball is attracted to the rod, but as soon as the two objects touch, the pith ball is repulsed from the rod. (a) Explain why the pith ball at first is attracted to the rod. (b) Explain why the pith ball is repulsed from the rod after it is touched by the rod.
4. Lightning usually occurs when negative charge in a cloud is transported to Earth. In the process the charge passes through the air, which is an insulator and goes to the ground, which is a conductor. If the Earth as a whole has a net charge of zero, explain what forces make the charge leave the cloud, pass through the air, and go to the ground.
5. Compare and contrast
Coulomb’s Law and Newton’s Law of Universal Gravitation.
(a) In what ways are the two laws similar? (b) In what ways are the two laws
different?
6. A certain pith ball is given a negative electric charge. A metal rod that is electrically neutral is brought near the charged pith ball but does not touch it. It is observed that the pith ball is attracted to the rod. Explain why this happens.
7. Suppose it is determined that a certain pith ball has a charge of – 4.00 ´ 10-17 C. Of which are there more in the pith ball, electrons or protons? Determine how many more.
8. How many coulombs of charge are on the electrons in a nickel coin? Follow this method to find the answer. (a) Find the number of atoms in a nickel coin. A nickel coin has a mass of 5.0 grams. Each mole (6.02 ´ 1023 atoms) has a mass of 58 grams. (b) Find the number of electrons in the coin. Each nickel atom has 28 electrons. (c) Find how many coulombs of charge are on the electrons. (d) Suppose this nickel then obtains a net charge of + 2.0 nC. Explain this net charge as a surplus or deficit of electrons and calculate how many. (e) What percent of atoms would have gained or lost a single electron in order for the nickel to get this net charge.
9. Two negatively charged bodies with –5.0 ´ 10-5 C are 0.20 m from each other. What force acts on each particle?
10. Two identical positive charges exert a repulsive force of 6.4 nN when separated by a distance of 0.38 nm. Calculate the charge of each.
11. A hydrogen atom consists
of one proton, mass 1.67 ´ 10-27 kg,
orbited by one electron, mass
9.11 ´10-31 kg.
The average distance between them is 5.3 ´
10-11 m. The proton and electron have the same amount of charge but
opposite signs (± e). (a)
Determine the magnitude of the electric force attracting one to the other. (b)
Determine the magnitude of the gravitational force attracting one to the
other. (c) Which force is stronger and by what factor? (And therefore is most
responsible for holding the electron in orbit about the proton)
12. Three charges are
arranged in a line as shown in the diagram below. (a) Determine the net
electric force on the middle charge. (b) Determine the net electric force on
the left charge.
13. Four charges are arranged in a square with sides equal to 10.0 cm. All four charges are equal to +2.5 nC. Determine the magnitude of electric force acting on any one of these four charges due to the presence of the other three.
14. Two pith balls, each
with mass 0.50 grams, are attached to one another by a string that is
20.0 cm long. The string is passed over a very thin wire so that the two balls
hang next to each other, just touching. A rubber rod is used to electrically
charge the two pith balls, after which the two balls repel one another. The
pith balls reach an equilibrium state of rest when their centers are 5.00 cm
apart. Determine the electric charge on each pith ball, assuming these values
to be equal.
15. Make a sketch of charges located in the x-y plane at the given coordinates: charge A = +7.50 mC at (-50.0 cm, 0.00 cm); charge B = -7.50 mC at (+50.0 cm, 0.00 cm); and charge C = +2.10 mC at (0.00 cm, +30.0 cm). Charges A and B are fixed in place and charge C is free to move. Given the mass of C is 2.50 grams determine its acceleration due to its electrical interaction with A and B.
16. A certain pith ball has a charge of +4.0 nC and is located at the origin of a coordinate system. Determine the electric field at the following points in the x-y plane: (a) (0.00 cm, -30.0 cm) and (b) (+15.0 cm, 0.00 cm). (c) Repeat both (a) and (b) for a charge of -4.0 μC located at the origin.
17. In a demonstration with a Van de Graaff generator two spheres are given opposite charges of +2.0 μC and -2.0 μC. Each sphere has a diameter of 30.0 cm and the centers of the spheres are 1.50 m apart. (a) Make a sketch of the electric field surrounding the two spheres. For the next two questions assume the two spheres produce fields equivalent to those produced by point sources (which is not exactly true). (b) Determine the electric field at a point exactly half way between the two spheres. (c) Determine the electric field at a point along a line connecting the centers and just above the surface of the negative sphere.
18. Air becomes a conductor
when the electric field strength exceeds 3000 kN/C. (a) Determine the
maximum amount of charge that can be carried by a metal sphere 0.15 m in
radius. (At this amount of charge, the field strength at the surface will be
just great enough to cause sparks to radiate outward from the sphere,
preventing further buildup of charge.)
(b) Determine the acceleration rate of an electron at the surface just as a
spark occurs.
19. Determine the electric field acting on charge C in problem #15. Note: you should be able to use your results from that problem in order to simplify this calculation.
20. Make a careful sketch of the electric field lines around the charges in problem #12. (No calculations.)
21. If 120 J of work are done to move one Coulomb of negative charge from a positive plate to a negative plate, what voltage difference exists between the plates?
22. How much work is done to transfer 0.15 C of charge through a potential difference of 9.0 V?
23. An electron is moved through a potential difference of 500 V. How much work is done on the electron?
24. A 12 V battery does 1200 J of work transferring charge. How much charge is transferred?
25. A force of 0.053 N is required to move a charge of 37 mC a distance of 25 cm in an electric field. (a) Determine the electric field strength, assuming it is constant. (b) What is the amount of potential difference between the two points?
26. The earth is surrounded by an electric field of 150 N/C pointing toward its center. This field can be assumed to be uniform and pointing downward within a classroom. (a) What electric charge would have to be placed on a 0.10 gram pith ball in order for it to “levitate” – i.e. float in air without moving? (b) Determine the potential difference between the ceiling and floor, which are separated by 3.0 m.
27. Consider the information from the previous problem. Suppose a 0.10 gram pith ball with electric charge -8.0 nC is dropped from the ceiling to the floor. (a) Determine the work done by the electric field. (b) Determine the difference in the impact speed of the ball that results from the presence of the electric field – in other words compare the impact speed caused by only gravity to the impact speed caused by both gravitation and electric force.
28. Two parallel metal plates are connected to a voltage source so that their potential difference is maintained at 350 V. The two plates are separated by 1.00 cm. An electron is released from rest at the negative plate and accelerates toward the positive plate. (a) Determine the electric field strength between the two plates. (b) Determine the amount of kinetic energy gained by the electron. (c) Determine the speed of the electron just as it reaches the positive plate.
29. A 12.0 V battery is connected to a 6.0 nF parallel plate capacitor. (a) What amount of charge will exist on each plate once electrostatic equilibrium is reached? (b) What amount of energy is “stored” in the capacitor in this state?
30. Each plate on a 3.75 nF capacitor carries a charge with a magnitude of 17.5 nC. (a) What is the potential difference across the plates? (b) If the plates are 0.65 mm apart, what is the magnitude of the electric field between the plates? (c) What amount of energy is stored?
31. In a certain application a capacitor is required to store 0.10 mJ of energy when operating at a voltage of 6.0 V. (a) Determine the capacitance needed for this application. (b) Determine the amount of charge stored at this voltage.
Selected Answers