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Exam1-f09-sol

Exam1-f09-sol - Physics 126 — Fall 2009 Midterm Exam#1...

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Unformatted text preview: Physics 126 — Fall 2009 Midterm Exam #1: Solutions October 8, 2009 xkcd.com The median score on this exam was 13/20. Questions 1 and 2 refer to the following situation. A proton (charge e = 1 . 6 × 10- 19 C) is moving parallel to a long, straight wire that carries a current I = 2 . 0 A. The proton is located a distance r = 4 . 0 cm from the wire and is moving with a speed of v = 6 . 5 × 10 6 m/s. I r v 1. What is the magnitude of the magnetic force on the proton? A) 7 . 7 × 10- 18 N B) 1 . × 10- 17 N C) 1 . 4 × 10- 17 N D) 2 . 1 × 10- 18 N E) 4 . 1 × 10- 18 N Solution: The magnetic field of the current-carrying wire is B = μ I/ 2 πr . At the location of the proton, the field points out of the page (use the RH rule: when your thumb points in the direction of the current, your fingers curl in the direction of the field). So the magnetic force on the proton is F B = evB = (1 . 6 × 10- 19 C)(6 . 5 × 10 6 m / s) (4 π × 10- 7 T · m / A)(2 . 0A) 2 π · . 040 m = 1 . × 10- 17 N . 2. Which vector best depicts the direction of the magnetic force on the proton? A) B) C) (into the page) D) (out of the page) E) Solution: The B-field at the location of the proton points out of the page, and the proton’s velocity vector points to the right. Apply the right-hand rule, pointing your thumb in the direction of the field and your fingers in the direction of the velocity. Your palm then points in the direction of the force, which is downward toward the wire. 3. A velocity selector is constructed by producing a constant E-field directed down- ward, and a constant B-field directed into the page as shown. The fields are adjusted so that charged particles with speed v = E/B pass through unde- flected. The effects of gravity are negligible. E q v B (into page) Which graph best represents how the magnitude of the acceleration experienced by a charged particle inside the velocity selector depends on the particle’s speed v ? A) v a v B) v a v C) v a v D) v a v E) v a v Solution: The net force is F E + F B = qE- qvB = qB ( E/B- v ) = qB ( v- v ). The acceleration is proportional to the net force ( F = ma ). Thus the acceleration is a linear function of v that is zero when v = v . Note that all the other choices have a nonzero acceleration for v = v ; this would not allow the particles with this “special” velocity to pass through undeflected. 4. You have a certain amount of material, which you form into a uniform wire with length L . You measure its resistance to be R . If you now take this same amount of material and form it into a wire with length 2 L , what is its resistance? A) 4R B) 2 R C) R D) R/ 2 E) R/ 4 Solution: You have a fixed amount of material, which means that the volume of the two wires is the same. The volume is the length times the cross-sectional area....
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Exam1-f09-sol - Physics 126 — Fall 2009 Midterm Exam#1...

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