Qualitative/quantitative translation (QQT)

Two conducting spheres joined by a wire

Units 9 and 10
8 points
About 18 minutes

You can use a calculator on this question, just like on exam day.

A shorter multipart problem that connects reasoning in words with an equation. You make and justify a claim without equations, derive an equation from a physics principle, and then explain whether the two agree or use them to predict what happens in a changed situation. On the exam: Question 4 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 15–20 minutes.

The question

Two conducting spheres are far apart and connected by a long, thin conducting wire. Sphere 1 has radius R, and sphere 2 has radius 3R. A total charge +Q is placed on the system, which then reaches electrostatic equilibrium. Ignore any charge on the wire, and treat each sphere as if the other were very far away.

Suggested time: 18 minutes

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Part (a)

3 points

(i) Does sphere 1 have more charge than, less charge than, or the same charge as sphere 2? (ii) Is the magnitude of the electric field just outside the surface of sphere 1 greater than, less than, or equal to that just outside sphere 2? Justify your answers. Do not use equations in this part; reason in words.

Your answer to part (a)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (b)

3 points

Derive expressions for the charge on each sphere, $q_1$ and $q_2$ , in terms of Q, and for the ratio $\dfrac{E_1}{E_2}$ of the field magnitudes just outside the surfaces of the spheres.

Your answer to part (b)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

Part (c)

2 points

Explain how your expressions from part (b) agree with your reasoning in part (a).

Your answer to part (c)

Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).

0 / 2,500 characters

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