Translation between representations (TBR)
Point charge at the center of a charged conducting shell
- Units 8, 9 and 10
- 12 points
- About 28 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem about one situation shown in several ways. You draw a diagram, derive equations, sketch or draw graphs, and then explain whether your answers agree with each other or use them to predict what happens when the situation changes. On the exam: Question 2 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 25–30 minutes.
The question
A point charge +Q is fixed at the center of a thick, spherical conducting shell with inner radius a and outer radius b. The shell has a net charge of −3Q. The system is in electrostatic equilibrium, and the electric potential is zero infinitely far away. Give answers in terms of Q, a, b, r, and physical constants (you may use ), as appropriate.
Suggested time: 28 minutes
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Part (a)
2 pointsDetermine the charge on the inner surface of the shell and the charge on the outer surface of the shell. Justify your answers.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
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Part (b)
3 pointsDerive expressions for the magnitude and direction of the electric field in each region: (i) r < a, (ii) a < r < b, and (iii) r > b.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
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Part (c)
3 pointsYou can’t draw here, so describe the graph you would sketch of the radial component of the electric field, (positive means outward), as a function of r from r = 0 to r = 3b. Describe each region, the sign of , and what happens at r = a and r = b.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
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Part (d)
2 pointsDerive expressions for the electric potential (i) at the outer surface of the shell, r = b, and (ii) at a point in the cavity a distance r from the center (r < a).
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
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Part (e)
2 pointsThe point charge is moved off center, but it stays inside the cavity and doesn't touch the shell. Does the electric field at points outside the shell (r > b) change? Justify your answer.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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