Solve 5 problems that probe your conceptual understanding of Coulomb's law and its implications.
Problem 1:
Two identical metal balls are suspended by insulating strings. Both balls have the same net charge. In this problem, do not assume the balls are point charges.
(a) Draw a separate free-body diagram for each ball. Label the forces to indicate:
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the object exerting the force, |
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the object on which the force is exerted, |
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the type of force (gravitational, normal, etc.), and |
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whether the force is a contact or a non-contact force. |
(b) Predict what will happen if the charge on the second ball is reduced slightly, so it is less than that on the first ball. Draw a sketch to illustrate your answer.
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Is the angle that ball 1 makes with the vertical, greater than, less than, or equal to the angle that ball 2 makes with the vertical? Explain your reasoning. |
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How does the free-body diagram for each ball in this case compare to the corresponding free-body diagram that you drew in part( a)? If the magnitudes or directions of any of the forces change, explain how they change. |
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Predict what will happen if the net charge on the second ball is reduced to zero. |
Problem 2:
Two point charges are held fixed in place as shown. One has positive charge + Q, the other has negative charge -Q. Another positive point charge +q is released from rest halfway between them.
Consider the following student comment about this situation: "There will be zero net force on the charge in the middle. Using Coulomb's law, the force due to the +Q charge is positive, and the force due to the -Q charge is negative. The forces cancel."
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Do you agree with the statement? Explain. |
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How does Coulomb's law apply to situations in which there are more than two point charges? |
Problem 3:
A rod of length L has a positive total charge + Q uniformly distributed along its length. Point P is to the right of the midpoint of the rod.
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What is the direction of the force on a positive test charge placed at point P? Explain how you determined your answer. How did you use the fact that the charge is uniformly distributed along the length of the rod to find the direction of the force at point P? |
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What is the approximate direction of the force on a positive charge placed at point R? Explain. |
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Explain how Coulomb's law may be applied to situations in which charge is distributed over an extended region, as is the case for the charged rod above. |
Problem 4:
A thin semicircular rod has a total charge + Q uniformly distributed along it. A negative point charge -Q is placed as shown. A test charge +q is placed at point C. Let FP and FR represent the force on the test charge due to the point charge and the rod respectively.
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Is the magnitude of FP greater than, less than, or equal to the magnitude of FR? Explain how you can tell. |
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Is the magnitude of the net force on +q greater than, less than or equal to the magnitude of FP? Explain. |
Problem 5:
A positive point charge +q is placed at point P to the right of two charges, A and B, which are fixed in place as shown. It is found that the net force on the +q charge is zero.
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What, if anything, can be said about the signs of charges A and B? Explain. |
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Does charge B "block" the effect of charge A at point P? Explain how you can tell. |
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What, if anything, can be said about the relative magnitudes of charges A and B? Explain. |
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Predict what would happen if a negative point charge were released from rest at point P instead of a positive point charge. Explain. |
To earn extra credit (1 point per problem) prepare a Word document containing your answers and email to mbreinig@utk.edu.