1997 Physics Olympiad Screening Test (21-30)

21. You are given two identical plano-convex lenses, one of which is shown to the right. When you place an object 20 cm to the left of a single plano-convex lens, the image appears 40 cm to the right of the lens. You then arrange the two plano-convex lenses back to back to form a double convex lens.

PO1997ques21diagram.gif (2330 bytes)

If the object is 20 cm to the left of this new lens, what is the approximate location of the image?

A. 6.7 cm to the right of the lens.
B. 10 cm to the right of the lens.
C. 20 cm to the right of the lens.
D. 80 cm to the right of the lens.
E. 80 cm to the left of the lens.

22. Positive charge Q is uniformly distributed over a ring of radius a that lies in the y-z plane as shown in the diagram.

PO1997ques22diagram.gif (1653 bytes)

The ring is centered at the origin. Which of the following graphs best represents the value of the electric field E as a function of x, the distance along the positive x axis?

PO1977ques22ans.gif (2682 bytes)

23. Four point charges are placed at the corners of a square with diagonal 2a as shown in the diagram.

PO1997ques23diagram.gif (1825 bytes)

What is the total electric field at the center of the square?

A. kq/a² at an angle 45º above the +x axis.
B. kq/a² at an angle 45º below the -x axis.
C. 3 kq/a² at an angle 45º above the -x axis.
D. 3 kq/a² at an angle 45º below the +x axis.
E. 9 kq/a² at an angle 45º above the +x axis.

Both questions 24 and 25 refer to the system shown in the diagram. A spherical shell with an inner surface of radius a and an outer surface of radius b is made of conducting material. A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell.

PO1997ques25diagram.gif (1858 bytes)

24. How is the charge -q distributed after it has reached equilibrium?

A. Zero charge on the inner surface, -q on the outer surface.
B. -Q on the inner surface, -q on the outer surface.
C. -Q on the inner surface, -q+Q on the outer surface.
D. +Q on the inner surface, -q-Q on the outer surface.
E. The charge -q is spread uniformly between the inner and outer surface.

25. Assume that the electrostatic potential is zero at an infinite distance from the spherical shell. What is the electrostatic potential at a distance R from the center of the shell, where b > R > a?

Use the circuit below to answer questions 26 and 27. B₁, B₂, B₃, and B₄ are identical light bulbs. There are six voltmeters connected to the circuit as shown. All voltmeters are connected so that they display positive voltages. Assume that the voltmeters do not effect the circuit.

PO1977ques2627diagram.gif (2941 bytes)

26. If B₂ were to burn out, opening the circuit, which voltmeter(s) would read zero volts?

A. none would read zero.
B. only V₂
C. only V₃ and V₄
D. only V₃, V₄, and V₅
E. they would all read zero

27. If B₂ were to burn out, opening the circuit, what would happen to the reading of V₁? Let V be its original reading when all bulbs are functioning and let V ' be its reading when B₂ is burnt out.

A. V ' > 2V
B. 2V > V ' > V
C. V ' = V
D. V > V ' > V/2
E. V/2 > V '

28. A particle with positive charge q and mass m travels along a path perpendicular to a magnetic field. The particle moves in a circle of radius R with frequency f. What is the magnitude of the magnetic field?

29. Two wires, each carrying a current i, are shown in the diagram to the right. Both wires extend in a straight line for a very long distance on both the right and the left. One wire contains a semi-circular loop of radius a centered on point X. What is the correct expression for the magnetic field at point X? HINT: The magnitude of the magnetic field at the center of a circular current loop of radius R is µ0 i/(2R).

PO1977ques29diagram.gif (1427 bytes)

PO1977ques29ans.gif (5446 bytes)

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

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

I. Moving the magnet toward the coil.
II. Moving the coil away from 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