8.2.P10
Some long molecules have charge distributions corresponding to alternating positive and negative source charges, as shown in this figure. The distance units are nanometers.
A professor measured the potential along a line of constant y-position for this molecule and obtained this graph of the electrostatic potential:
1. According to the potential shown in the graph (using it as shown, whether it correctly corresponds to the diagram or not!), if a test electron were released at the following positions along the x-axis, in what direction would the x-component of the electric force it feels point? (Use L for left, R for right, and 0 for there is no x-component.)
A. x = 6 nm
B. x = 1.5 nm
C. x = -6 nm
2. Which of the following statements could be true?
A. This potential was measured along the horizontal line that passes through the charges (y = +1 nm).
B. This potential was measured along the horizontal line 1 nm below the charges (y = 0 nm).
C. This potential was measured along the horizontal line 1 nm above the charges (y = +2 nm).
D. The professor was working too late and switched the plus and minus x-coordinates when he recorded the results (left and right are reversed).
E. The magnitude of the potential is largest at approximately x = -4.5 nm, y = 2.5 nm.
F. The potential measurement shown in the second figure indicates that the electric field is pointing up and to the right in the neighborhood of x = 5 nm, y = 0 nm.
G. The potential measurement shown in the second figure indicates that the electric field is pointing down and to the left in the neighborhood of x = 5 nm, y = 0 nm.
3. Suppose a Na+ ion approached this potential from the right along the x-axis and was constrained to move along the x-axis (no y-motion allowed). If it had very little KE but was moving slowly to its left when it was at the point x = 15 nm, and if there it essentially felt V = 0 from the molecule, how far along the axis would it come?
A. It would not be attracted, it would be repelled and travel to larger values of x.
B. It would stay where it was.
C. It would be attracted and come in to about 3.5 nm (the bottom of the well).
D. It would be attracted and come in to about 2 nm before bouncing back.
E. It would get about to 0.5 nm and bounce back.
F. Something else? Explain.
4. For the set of 8 source charges in the figure at the top, is there an equipotential line (really part of a surface in three dimensions) that corresponds to V = 0? If so, where is it? Select your answer(s) and fill in the blank if the answer you select has a blank to fill in:
A. No. There is none.
B. Yes. It is a vertical line going through x = _____
C. Yes. It is a horizontal line going through y = _____
D. Yes. It is a curved loop enclosing all the charges.
E. Yes. It is something else. (Describe it: _____________________)
5. It looks from the graph like the position x = 0 is not the local maximum, which is evidently a little to the left. If the diagram matches the graph would this be correct?
A. Yes
B. No
C. It's impossible to tell
Bill Dorland and Joe Redish 3/16/17
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