This test is 120 minutes long.
[10 points] 1. A moving charge in a magnetic field.
[5 points] (a) In a certain region there is a uniform magnetic field in the -y direction as shown below. A positive charge with a velocity in the +x direction experiences a force in which direction because of this field?
[5 points] (b) For the situation described above, the positive charge would follow a circular path; we now want the charge to move along a spiral around a line parallel to the y axis. Draw a vector diagram (similar to the one above) showing the directions of v and B necessary to accomplish this.
[25 points] 2. DC Circuits.
You have some wire, one 6 V battery, and three 8 ohm resistors.
[5 points] (a) Draw a circuit with the battery and resistors so that each resistor receives the same current. Note that there is more than one solution; you only need to draw one.
[7 points] (b) Calculate the current through one of the resistors in your circuit in part (a).
[5 points] (c) Now draw a circuit with the battery and resistors arranged so the current through one resistor is twice as large as the current through each of the other two. Again there is more than one solution; you only need to draw one.
[8 points] (d) How much power is provided by the battery in your circuit in part (c)?
[25 points] 3. Two charged spheres.
Two hollow conducting spheres, one with radius 5 cm and one with radius 10 cm, are arranged about a common center. The inner sphere has a charge of +3.00 microCoulombs uniformly distributed over its surface; the outer sphere has a uniformly-distributed charge of -2.00 microCoulombs.
[6 points] (a) On the diagram, sketch the electric field produced by the spheres.
[5 points] (b) The point P in the diagram is 12 cm from the center of the spheres. Using a dashed line, draw the equipotential line that passes through P.
[6 points] (c) What is the electric potential at a distance of 12 cm from the center of the spheres?
[8 points] (d) A charged particle is fired directly at the spheres from a point a long way to the right. It slows down as it approaches the spheres, comes to a stop at point P, and is then repelled away from the spheres. The particle has a mass of 2 x 10-4 kg, and a speed, when it is very far from the spheres, of 60 m/s. What is the sign and magnitude of the charge on the particle?
[25 points] 4. Induction.
A coil consists of 128 turns of wire wrapped around a square frame 0.3 m on a side; the coil has a total resistance of 1.8 ohms. The coil is located in a region where there is a constant magnetic field B = 0.8 T. Initially, the field is perpendicular to the plane of the coil.
[5 points] (a) What is the magnetic flux through one turn of the coil in the starting orientation?
[10 points] (b) The coil is rotated until the magnetic field is in the plane of the coil. The rotation is done in such a way that the emf induced in the coil is constant during the motion, which takes 3.0 seconds. What is the magnitude of the induced emf during this rotation?
[10 points] (c) The wires from the coil are connected to a meter that measures the total charge that flows through it during the rotation. How much charge flows?
[25 points] 5. Refraction.
A light ray traveling through some plastic has a frequency of 5.5 x 1014 Hz. It is incident upon a flat slab of glass, making an angle of 32° with the normal to the interface; it passes through the glass and into vacuum, as shown in the sketch. The refractive index of the plastic is 1.50. The refracted ray in the glass has a wavelength of 321 nm.
[5 points] (a) What is the refractive index of the glass?
[10 points] (b) What is the angle of refraction (measured from the normal) for the light ray in vacuum?
[10 points] (c) What is the minimum angle of incidence (in plastic) for which the ray will be totally internally reflected at the glass-vacuum interface?
[10 points] 6. Refraction and reflection.
Three parallel rays are incident on a converging lens; the lens has a focal length of 3.0 cm. In each of the two cases below, draw the path of each light ray and state the x and y coordinates of the point where the rays converge.
Assume the lens lies at the origin of an x-y coordinate system, and the grid has a spacing of 1 cm by 1 cm.
[5 points] (a) The rays are parallel to the principal axis, and shine on the upper half of the lens.
The rays converge at: x = ______ cm y = ______ cm
[5 points] (b) The rays are parallel to the principal axis; a plane mirror is placed at x = 2 cm, parallel to the y-axis.
The rays converge at: x = ______ cm y = ______ cm
[25 points] 7. The double slit.
Two very narrow parallel slits separated by a distance d1 = 1.0 mm are illuminated with monochromatic light with a wavelength of 400 nm. An interference pattern is observed on a screen 1.3 m away.
[8 points] (a) What is the distance between the central and first interference maxima on the screen?
[6 points] (b) Suppose the distance between the slits is increased slightly to a value d2. The separation between the central and first interference maxima will:
[ ] increase
[ ] decrease
[ ] stay the same
[6 points] (c) The wavelength of light is now changed to 630 nm; the slit separation is still at the unknown increased distance d2. It is found that the separation between the central and first interference maxima is the same value obtained in part (a) (i.e., when the wavelength was 400 nm, and the slits were 1.0 mm apart). What is the value of the current slit separation d2?
[5 points] (d) Suppose thge entire apparatus is now immersed in a transparent medium with refractive index greater than 1. The separation between the central and first interference maxima will:
[ ] increase
[ ] decrease
[ ] stay the same
[25 points] 8. The photoelectric effect.
The work function of a metal surface is 2.48 eV. The metal surface is illuminated by a light source.
[5 points] (a) Find the minimum frequency that light must have to eject electrons from the surface of this metal.
[5 points] (b) The metal surface is illuminated by a light source with a wavelength of 600 nm. Are any photoelectrons emitted from the metal surface?
[10 points] (c) The metal surface is now illuminated by a light source with a wavelength of 400 nm. What is the maximum kinetic energy of the emitted photoelectrons?
[5 points] (d) The intensity of the light source is doubled, without changing its wavelength. What is the maximum kinetic energy of the emitted photoelectrons now?
[20 points] 9. Light.
[6 points] (a) A light source emits 100 W of red light. A second light source emits 1 W of green light.
Which of these light sources is emitting photons of greater energy?
[ ] red
[ ] green
Which of these light sources is emitting the greater number of photons in a second?
[ ] red
[ ] green
[9 points] (b) A hydrogen atom emits light when an electron jumps from the n = 2 Bohr energy level to the ground state. Find the wavelength of the emitted light.
[5 points] (c) A glass plate (refractive index n = 1.60) is coated with a thin film of magnesium fluoride (refractive index 1.38) to make it nonreflecting for normally incident light of wavelength 550 nm in air. What is the minimum thickness t of the film?
[10 points] 10.
[5 points] (a) A wooly mammoth bone found in an archeological dig is sent to a laboratory to determine its age. Analysis shows that there are an average of 2 decays per minute per gram of carbon, from the radioactive decay of carbon-14 in the bone. Normal living organisms exhibit 16 decays per minute per gram of carbon. Assuming that the bone had the normal concentration of carbon-14 when the mammoth died, what is the approximate age of the bone? The half-life of carbon-14 is 5700 years.
[5 points] (b) Within the core of a nuclear reactor there are 3 x 1019 nuclei fissioning each second. The energy released by each fission is about 200 MeV. Determine the power (in watts) being generated.