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.

 

 

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

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.

 

 

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?

 

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

 

 

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

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.

 

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

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.

 

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

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  What is the magnitude of the magnetic field?

 

29. Two wires, each carrying a current i, are shown in the diagram below.

 

 

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?

 

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

 

 

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