UNIVERSITY OF BRITISH COLUMBIA

Science 1 Physics

Sessional Examination

9 April 2001

Time: 2${1\over2}$ hours

Instructors: Jess H. Brewer & Domingo Louis-Martinez

1.

``QUICKIES''   [40 marks - 5 each]

(a)

A 50 kg woman is standing still on the Moon. Approximately what net force does she exert on the Moon?
(i) 50 kg (ii) 500 N (iii) 20 N (iv) 0 N

(b)

Two large meteors made of pure carbon collide just outside the Earth's atmosphere and produce a huge number of ``buckyballs'' (C₆₀ molecules) that then fall gently into the atmosphere and settle toward the ground. One buckyball has a mass of $1.1956 \times 10^{-24}$ kg. After the buckyballs have had plenty of time to reach thermal equilibrium, assuming perfectly still air at 300 K, at what altitude above sea level will the concentration of buckyballs (per cubic meter of air) be exactly 1/e of their concentration at sea level? (Here e is the base of the natural logarithm.)

(c)

Some butterflies have bright blue wings without any blue pigments. Explain briefly how this is possible.

(d)

A velocity selector has a magnetic field $\vec{\mbox{\boldmath$B$\unboldmath }}$ perpendicular to an electric field of 10,000 V/m. We find that charged particles with velocity $v = 2.0 \times 10^4$ m/s perpendicular to both $\vec{\mbox{\boldmath$E$\unboldmath }}$ and $\vec{\mbox{\boldmath$B$\unboldmath }}$ pass through the device undeflected. What is the strength of $\vec{\mbox{\boldmath$B$\unboldmath }}$ [in Tesla]? Explain.

(e)

A diffraction grating is uniformly illuminated, producing the interference pattern shown below on a distant screen.
 
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i) How many slits are illuminated?
ii) What is the ratio of the width of each slit to the spacing between adjacent slits?

(f)

If $\epsilon_\circ$ and $\mu_\circ$ are respectively the permittivity and the permeability of free space, what is the value [including units] of the quantity $(\mu_\circ \epsilon_\circ)^{-1/2}$ and what does it represent?

(g)

Suppose you have a superconducting coil, a capacitor and a 1000 $\Omega$ resistor. First you charge up the capacitor and put it in series with the coil; this circuit oscillates at a frequency of $f = (1/2\pi)$ kHz. Next you charge up the same capacitor and discharge it through the resistor. (No coil in the circuit this time.) It takes 0.1 s for the charge on the capacitor to drop to  1/e  of its original value. What was the inductance of the coil?

(h)

An electron is trapped between two parallel flat plates 5 nm apart. What is the lowest kinetic energy it can have?

2.

Cylinder of Charge   [12 marks] A long solid insulating cylinder of radius R is uniformly charged with a positive charge density $\rho$ [charge per unit volume]. A small hole is drilled straight through the cylinder at right angles to its axis, as shown. Assume that the hole is very far from the ends of the cylinder.
 
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(a)

[6 marks] Show that the electric field in the hole is proportional to the distance from the cylinder axis.

(b)

[6 marks] Show that a negatively charged particle dropped straight into the hole will execute simple harmonic motion as long as it doesn't hit the sides of the hole.

3.

Field of a Wire   [12 marks] A wire (i.e. a long, straight, solid cylindrical conductor) of radius R carries a steady current $I_\circ$ that is uniformly distributed over the cross-sectional area of the wire.
 
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Calculate the magnetic field $\vec{B}$ at a distance r from the centre of the wire in both regions: $r \ge R$ and r < R.   Sketch B(r) from r=0 to r=4R.

4.

Falling Bar   [12 marks] A horizontal bar of mass m is free to slide without friction down the vertical rails of a conducting frame, as shown. The combined resistance of the bar and the frame is negligible compared to R, the resistance placed in series with this circuit. What is the terminal speed of the bar as it falls under the influence of gravity (at the surface of the Earth) through a uniform horizontal magnetic field $\vec{\mbox{\boldmath$B$\unboldmath }}$ directed perpendicular to the plane of the frame? (Give your answer in terms of m, B, $\ell$, R, g and other fundamental constants.)
 
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5.

Relativistic Reflection   [12 marks] A rocket moves at constant speed u toward a stationary mirror. When the rocket is a distance d from the mirror (as measured by an observer at rest with respect to the mirror) a light pulse is emitted from the rocket toward the mirror and is subsequently reflected back to the rocket. What is the total travel time of the light pulse as measured by

(a)

[6 marks] an observer in the rest frame of the mirror?

(b)

[6 marks] an observer in the rest frame of the rocket?

6.

Current Ring   [12 marks] An electric current I is circulating as shown around a superconducting ring of radius R. What is the magnetic field on axis a distance z up from the centre of the ring, in terms of the parameters given?
 
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