1996 Physics Olympiad Screening Test (21-30)

21. Two mirrors, labeled L_M for left mirror and R_M for right mirror in the accompanying figure, are parallel to each other and 3.0 m apart. A person standing 1.0 m from the right mirror (R_M) looks into this mirror and sees a series of images.

PO1996ques21diagram.gif (1735 bytes)

How far from the person is the second closest image seen in the right mirror (R_M)?

A. 2.0 m
B. 4.0 m
C. 6.0 m
D. 8.0 m
E. 10.0 m

22. A thin film of thickness t and index of refraction 1.33 coats a glass with index of refraction 1.50.

PO1996ques22diagram.gif (1622 bytes)

What is the least thickness t that will strongly reflect light with wavelength 600 nm? Hint: Light undergoes a 180º phase shift when it is reflected off a material with a higher index of refraction.

A. 225 nm
B. 300 nm
C. 400 nm
D. 450 nm
E. 600 nm

23. The accompanying figure shows two concentric spherical shells isolated from each other. The smaller shell has radius b and net charge +Q. The larger shell has radius 2b and an equal net charge +Q.

PO1996ques23diagram.gif (2082 bytes)

If R is the distance from the common center, the highest electric field magnitude E occurs:

A. only at R = 0, where E is infinite.
B. anywhere R < b, where E is constant
C. immediately outside the smaller (R = b) shell.
D. immediately outside the larger (R = 2b) shell.
E. far away from the shells; E increases with distance.

24. An infinite conducting plate of thickness 0.0200 m is surrounded by a uniform field E = 400 V/m directed left to right.

PO1996ques24diagram.gif (2623 bytes)

Let the potential V_o = 0 a distance 0.0200 m to the right of the plate. What is V₃, the potential 0.0300 m to the left of the plate?

A. - 28 V
B. - 20 V
C. + 12 V
D. + 20 V
E. + 28 V

25. A sphere of radius a has uniform charge density r. A spherical cavity of radius c is formed in the sphere. The cavity is centered a distance b (b>c) from the center of the sphere.

PO1996ques25diagram.gif (1843 bytes)

What is the magnitude of the electric field at the center of the cavity?

PO1996ques25ans.gif (3289 bytes)

26. As shown in the diagram, two fixed charges, q₁ = +1.00 mC and q₂ = - 4.00 mC, are 0.200 m apart.

Where is the total field zero?

A. 0.40 m to the right of q₁
B. 0.13 m to the right of q₁
C. 0.1m to the right of q₁
D. 0.067 m to the left of q₁
E. 0.20 m to the left of q₁

27. The switch is closed in the circuit shown.

PO1996ques27diagram.gif (2005 bytes)

What is the charge on the capacitor when it is fully charged?

A. 5.0 mC
B. 10 mC
C. 20 mC
D. 40 mC
E. 60 mC

28. Two identical resistors with resistance R are connected in the two circuits drawn below.

PO1996ques28diagram.gif (2089 bytes)

The battery in both circuits is a 12 volt battery. Which statement is correct?

A. More current will flow through each R in circuit I than in circuit II.
B. More total power will be delivered by the battery in circuit II than in circuit I.
C. The potential drop across each R will be greater in circuit I than in circuit II.
D. The equivalent resistance will be greater in circuit II than in circuit I.
E. The power dissipated in each R will be greater in circuit I than in circuit II.

29. The resistors – R₁, R₂, and R₃ – have been adjusted so that the current in the ammeter (labeled A in the accompanying circuit diagram) is zero.

PO1996ques29diagram.gif (2053 bytes)

What is R?

A. R₂
B. R₃
C. R₁ R₂ /R₃
D. R₁ R₃ /R₂
E. R₂ R₃ /R₁

30. A long cylindrical conducting wire – shown in cross section to the right – carries a conventional current out of the page. The wire has uniform current density J and radius a.

PO1996ques30diagram.gif (1593 bytes)

What is the magnetic field inside the wire, a distance R (R<a) from the wire’s center?

A. ½ m_oJa clockwise
B. ½ m_oJa²/R clockwise
C. ½ m_oJR counterclockwise
D. ½ m_oJa²/R counterclockwise
E. ½ m_oJa counterclockwise