SMC PHYSICS 9 — MIDTERM 3 — Fall 2002 page 1

Question 1: (10 pts) Show the direction of the loop’s induced current in each of the following situations, at the moment shown.

Question 2: (10 pts) A coil is made of 25 circular loops of wire. The total resistance of the coil is 0.85 . The coil is face-on to a magnetic field that varies with time, given by B(t) = 2 + 6t - t2.

At time t = 2.0 s, the coil has a current of 1.50 A induced in it.

a) What is radius of each loop?

b) What is the induced voltage in the loop at any time t? (The variable “t” will be in your answer.)

c) Does the current ever equal zero? If so, when? If not, why not?
Question 3: (8 pts) In the situations below, show the direction of the magnetic force felt by the indicated objects.


Question 4: (8 pts) A compass usually points “north”. When placed directly on top of a current carrying wire, the compass is deflected from north by 30°, as shown. How much current flows in the wire, and in which direction? (BEarth = 5.0 x 10-5 T)

Question 5: (9 pts) Draw THREE rays in each of the following situations to find the image.


Question 6: (5 pts) Draw a sketch to find the image AND calculate its position and height, given that the object’s height is 2.0 cm, it is 8.0 cm from the mirror, and the mirror has a radius of 10.0 cm.

Question 7: (5 pts) Draw a sketch to find the image AND calculate its position and height, given that the object’s height is 2 cm, it is 25 cm from the lens, and the lens has a focal length of 10 cm.

Question 7: (12 pts) Continue the two light rays on the figure below to show where they will go next (find the actual angles). (ndiamond = 2.42; nair = 1.00)

Continue the two light rays on the figure below to show where they will go next (find the actual angles). (ndiamond = 2.42; ncarbon disulfide = 1.63)


Question 8: (3 pts) Which way will the current carrying loop rotate if released at rest at the position shown?

Question 9: (5 pts) Rank the magnetic fluxes, from most flux to least flux, passing through the loops in the following situations. (The value of B given is what is important, NOT the exact number of “x”’s shown.)

Question 10: (10 pts) Uranium nuclei have either 235 or 238 protons/neutrons - these are different “isotopes” of uranium. Only U-235 can be used in an atomic bomb. A uranium sample (containing both U-235 and U-238) is vaporized and the atoms are then ionized, each losing one electron. The charged uranium isotopes are then accelerated by an electric field.

a) Each atom is given kinetic energy equal to 8.00 x 10-16J. What speeds do the U-235 and U-238 have?

b) Which did you expect to be moving fastest in part a)? Why?

c) Now the uranium ions enter a uniform magnetic field of strength B = 0.25 T. Which of the isotopes do you expect to travel in a smaller radius circle? Why? (Careful!)

d) What are the actual radii that the two isotopes travel in, and how far apart would the two beams leave the magnetic field (“d”, as shown above)?

FORMULAE:

B = (o/4) qvsinr2Bwire = oI/2rBloop = oI/2r = NBA cos

F = ILBF = qvBsinF = ma = - d/dt

 = I RP = I V = I2R = V2/R

K = ½ mv2U = q V F = maF = mv2/r

1/p +1/q = 1/ffspherical mirror = R/2M = -q/p = h’/hn1sin1n2sin2

CONSTANTS:

h = 6.63 x 10-34 Jsħ= h/2me = 9.11 x 10-31 kg

c = 3.00 x 108 m/se = 1.6 x 10-19 Cmproton = mneutron = 1.67 x 10-27 kg

g = 9.8 m/s21 eV = 1.6 x 10-19 Jk = 9 x 109 Nm2/C2

C = 2RA = R2