Physics 122 Practice Midterm Exam #2

Physics 122 Practice Midterm Exam #2

8 November 2019

If this were a real exam, you would be told the exam rules: "You may consult only one page of formulas and constants, a calculator, and your Biot-Savart tinkertoy model while taking this test. You may not consult any books, nor online or digitally-stored resources, nor each other. All of your work must be written on the attached pages, using the reverse sides if necessary. The final answers, and any formulas you use or derive, must be indicated clearly. Exams are due 50 minutes after we start, and will be returned to you within the week. Good luck. "Note: ? "There are four problems in the following pages. You need only complete three of

these problems, of which one must be Problem #1.

? "You can attempt more than three problems points worth; we will grade you on your best three complete problems.

? "Work first on the problems you find easiest, and come back to harder or less familiar material later. Don't get stuck.

? "The amount of space left for each problem is not necessarily an indication of the amount of writing it takes to solve it.

? "If you need a physical constant or formula that is not on your cheat sheet, don't give up: estimate its value. If your estimate is reasonable you will lose few or no points.

? "On that same theme: remember that you can earn partial credit for being on the right track. Be sure to show enough of your reasoning that we can figure out which track you're on."

Your name (please print clearly): ______________________________ Time and place of your workshop: ______________________________

Problem 1 (40 points) A hexagonal wire loop with side 2a carries a current I. Derive a formula for the magnetic field (magnitude and direction) at the center of the loop. Show all your work, deriving any formulas you may need.

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Problem 1 (continued) - 3 -

Problem 2 (30 points) Two infinite, planar sheets of current, viewed edge-on at right, are perpendicular. They carry equal current per unit length K, directed out of the page. Calculate the magnetic field (magnitude and direction) along the plane 45? from both currents, indicated by the dashed line in the diagram at right. Show all your work, deriving any formulas you may need.

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Problem 2 (continued) - 5 -

Problem 3 (30 points)

No current runs in the circuit at right; then, at t = 0, the switch S is closed. Both resistors have value R; the inductor L; the battery .

(a) What current is drawn from the battery just after t = 0?

(b) Derive a formula for the current in the inductor as a function of time.

(c) What is the energy stored in the inductor, after the switch has been closed a long time?

Show all you work, deriving any formulas you may need.

S

R

R

L

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Problem 3 (continued) - 7 -

Problem 4 (40 points)

A single circular loop of wire r = 1 cm in radius is placed inside a long solenoid, R = 3 cm in radius, with its plane perpendicular to the axis of the solenoid. The solenoid has n = 200 turns per cm.

(a) Suppose the solenoid carries a current I = I0 cost, where I0 = 5.0 amp and = 120 radians s-1. Evaluate the emf induced in the smaller loop as a function of time.

(b) Suppose instead that the solenoid carries a constant current of IS = 5.0 amp , the loop carries a constant current of IL = 1.0 amp , and the two currents flow in opposite directions. How much work does an external agent need to exert, or receive, to rotate the loop 180? about a diameter?

r = 1 cm R = 3 cm

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