Mathematical routines (MR)
Field and potential on the axis of a charged ring
- Units 8 and 9
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem where you use math, including calculus, to analyze a physical situation. You draw or sketch a representation such as a diagram or a graph, derive an equation using letters, calculate a numerical answer with units, and make a claim or prediction and justify it with physics reasoning. On the exam: Question 1 of 4. Section II has 4 questions in 95 minutes (50% of the exam score), one of each type in this order; calculator and equation sheet allowed. The CED suggests 20–25 minutes.
The question
A thin ring of radius R has a total charge +Q spread uniformly around it. The ring lies in the yz-plane with its center at the origin, so the x-axis is the ring's axis. The electric potential is zero infinitely far away.
Suggested time: 22 minutes
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Part (a)
2 pointsDerive an expression for the electric field (magnitude and direction) at a point on the x-axis a distance x from the center of the ring (x > 0).
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (b)
2 pointsDerive an expression for the electric potential at the same point on the x-axis.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
2 pointsThe ring has Q = 5.0 nC and R = 0.10 m. A proton starts very far away on the x-axis and moves directly toward the ring. Calculate the minimum initial speed the proton needs to reach the center of the ring.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (d)
2 pointsYou can’t draw here, so describe the graph you would sketch of the x-component of the electric field, , as a function of x, from x = −3R to x = 3R.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (e)
2 pointsA student claims that, because the electric field is zero at the center of the ring, the electric potential there must also be zero. Do you agree or disagree? Justify your answer.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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