Aim for FivePhysics C: E&M

Translation between representations (TBR)

A square loop pulled through a magnetic field

  • Unit 13
  • 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 square conducting loop with side length s and resistance R lies in the plane of the page and is pulled to the right at constant speed v. It passes through a region of uniform magnetic field of magnitude B directed into the page. The field region has sharp edges at x = 0 and x = 2s and extends far above and below the loop; outside the region the field is zero. The loop's top and bottom sides stay horizontal. At time t = 0 the loop's right (leading) side reaches x = 0.

Suggested time: 28 minutes

Your answers are saved in this browser as you type.

Something wrong with this question?

What's wrong?

Please don't include personal details.

Part (a)

2 points

Derive expressions for (i) the magnetic flux through the loop and (ii) the magnitude of the induced emf, while the loop is entering the field (0 < t < s/v).

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

0 / 2,500 characters

Part (b)

4 points

You can’t draw here, so describe the graphs you would sketch on separate axes, from t = 0 to t = 4s/v: (i) the magnetic flux through the loop as a function of time, and (ii) the induced current as a function of time, taking counterclockwise current as positive. Give values and the times where the graphs change.

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

0 / 2,500 characters

Part (c)

1 point

Explain why the induced current is counterclockwise while the loop is entering the field.

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

0 / 2,500 characters

Part (d)

2 points

Derive an expression for the magnitude of the external force needed to keep the loop moving at constant speed while it is entering the field, and state its direction.

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

0 / 2,500 characters

Part (e)

2 points

Show that, while the loop is entering the field, the rate at which the external force does work equals the rate at which thermal energy is produced in the loop.

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

0 / 2,500 characters

Part (f)

1 point

The experiment is repeated with the loop pulled at speed 2v. Does the total thermal energy produced while the loop passes completely through the field increase, decrease, or stay the same? By what factor? Justify your answer.

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

0 / 2,500 characters

Checking scoring…

Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.