1993 Physics Olympiad Screening Test (21-30)

21. Two small identical conducting spheres are separated by a distance much larger than their diameter. They are initially given charges of -2.00 x 10^-6 C and +4.00 x 10^-6 C, and found to exert a force on each other of magnitude 1.000 N. Without changing their position, they are connected by a conducting wire. When the wire is removed, what is the magnitude of the force between them?

A. 0
B. 0.125N
C. 0.250 N
D. 1 .000 N
E. 1.125N

22. Charges of ±Q, with Q = 2.0 x 10^-7 C, are placed at three corners of a square whose sides are 0.10 m. The magnitude of the total field at the center of the square is:

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A. 5.1 x l0³ V/m
B. 2.5 x l0⁴ V/m
C. 7.5 x l0⁴ V/m
D. 3.6 x l0⁵ V/m
E. 1.08 x l0⁶ V/m

23. Three 60 W light bulbs are mistakenly wired in series and connected to a 120 V power supply. Assume the light bulbs are rated for single connection to 120 V. With the mistaken connection, the power dissipated by each bulb is:

A. 6.7 W
B. 13.3 W
C. 20 W
D. 40 W
E. 60 W

24. Two thin spherical conducting shells are centered on the same point. The inner sphere has radius b and total charge q. The outer sphere has radius B and total charge Q. At a point a distance R from the common center, where b<R<B, and assuming the electric potential is zero an infinite distance away, the total potential due to the two spheres is:

A. kq / b + kQ / B
B. kq / b + kQ / R
C. kq / R
D. kq / R + kQ / B
E. kq / R + kQ / R

25. What is the magnitude of the total electric field for the two spheres at the point described in the preceding question (#24)?

A. kq / b² + kQ / B²
B. kq / b² + kQ / R²
C. kq / R²
D. kq / R² + kQ / B²
E. kq / R² + kQ / R²

26. A current of 0.10 A flows through the 25 W resistor represented in the diagram below.

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The current through the 80 W resistor is:

A. 0.10 A
B. 0.20 A
C. 0.30 A
D 0.40 A
E. 0.60 A

27. The circuit shown in the accompanying figure has been connected for a very long time.

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The voltage across the capacitor is:

A. 1.2 V
B. 2.0 V
C. 2.4 V
D. 4.0V
B. 6.0 V

28. The accompanying sketch represents a bubble chamber photograph. The magnetic field is directed out of the plane of the sketch. All particles have the same velocity initially from left to right.

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The one that is most likely an electron is:

A. A
B. B
C. C
D. D
E. E

29. What is the correct expression for the magnetic field at point X in the diagram shown below?

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HINT: The magnitude of the magnetic field at the center of a circular current loop of radius R is m_oi/(2R)

A.
B.
C.
D.
E.

30. You are given a bar magnet and a looped coil of wire.

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Which of the following would induce an emf in the coil?

I. Moving the magnet away from the coil.
II. Moving the coil toward the magnet.
III. Turning the coil about a vertical axis.

A. I only
B. II only
C. I & II
D. I & III
E. I, II, III