Physics 204 Mid Term

Lecturer: Dr. Min Xu

Nov 3, 2003
LAST NAME: ___________________________________________________________________________________________________ FIRST NAME: __________________________________________________________________________________________________ SS# (last 4 digits): _____________________________________________________________________________________________

General Instruction

You have 1 hour 30 minutes to answer 7 questions on this exam. Work each problem only on the sheet provided for this problem, using the back if necessary. Please write the name and recitation section on each sheet at the top of the page.

You must indicate the reasoning and show all the steps.

If you are unable to obtain the answer to part of a problem and you need the answer to solve the subsequent parts, use an appropriate symbol for the answer to the previous part and solve in terms of that symbol.

Some useful constants and formulas are given here:

me = 9.1 × 10 -31kg -7 m0 = 4p × 10 W b/A .m e0 = 8.85 × 10 -12C2/N .m2 -19 e = 1.60 × 10 C -1--- = 9.0 × 109N .m2/C2 4pe0 B = m0I/(2pr) F = qvB sin(h) F = ILB sin(h) e = -N DP/Dt

1. (5 points) A charged particle, passing through a certain region of space, has a velocity whose magnitude and direction remain constant. (a) If it is known that the external magnetic field is zero everywhere in this region, can you conclude that the external electric field is also zero? Explain. (b) If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field is also zero? Explain.

2. (5 points) A copper rod is dragged through a uniform magnetic field B with a velocity v as displayed in the following figure. Which end of the rod has a higher electric potential? What happens if the rod is wooden instead? The length of the rod is L.

PIC

3. (5 points) Deduce the direction of the induced current in the coil when the magnetic bar is moving closer to the coil (see the following figure). Provide your reasoning. PIC

4. (5 points) The coil of a motor shall burn most probably when the motor is starting up. Why?

5. (20 points) Consider a multiloop circuit shown in the following figure. The battery has an emf V = 10V and all the resistors have resistance of R1 = R2 = R3 = R4 = 1_O_.


(a) (5 points) Find the effective resistance of the circuit.
(b) (5 points) Find the current through the resistor R1.
(c) (5 points) What is the potential difference V ce between the points c and e?
(d) (5 points) What is the power consumption by the resistors R1 and R2.

PIC

6. (20 points) Three very long parallel straight wires are arranged as shown in the figure. Wires A and C carry equal currents of 10A, and B carries a current of 20A, with the current at C pointing into the page while those at A and B point out of the page. AB and AC are perpendicular to each other, i.e., ABC is a right angle triangle with equal sides.


(a) (9 points) Find the direction and the magnitude of the magnetic fields BA, BB and BC at P, the midpoint between A and C, by the current A, B and C.
(b) (6 points) Find the total magnetic field at that point P (direction and magnitude).
(c) (5 points) Find the magnitude and direction of the force on a positive charge q = 1 × 10-18C that is at P and moving with a velocity of 2.0 × 106m/s directed out of the page.

PIC

7. (15 points) A charged particle moves through a velocity selector at a constant speed in a straight line. The electric field of the velocity selector is 4 × 103N/C, while the magnetic field is 0.4T.


(a) (5 points) What is the direction of the electric field? Mark the electric field in the figure.
(b) (7 points) When the electric field is turned off, the charged particle travels on a circular path whose radius is 4cm. Find the charge-to-mass ratio of the particle.
(c) (3 points) What is the polarity of the charge (positive or negative) if the charged particle moves in a anti-clockwise direction on the circular path when the electric field is turned off?

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8. (25 points) A conducting rod slides down between two frictionless vertical copper tracks. There is no kinetic friction between the rod and the tracks, although the rod maintains electrical contact with the tracks during its fall. A constant magnetic field B = 1T is directed perpendicular to the motion of the rod. A resistance R = 1_O_ is connected between the tops of the tracks. The rod has a weight W = mg where m = 0.1kg and g = 10m/s2 due to gravity. The length of the rod is L = 1m. The rod starts to fall from the position x0 = 0 from rest and moves in the positive direction of the x-axis.


(a) (5 points) Will the rod fall with the acceleration g (free fall)? Explain.
(b) (5 points) The speed of the rod shall increase and reach a constant value vf during the fall. What is the change of the magnetic flux through the loop in a unit time when the rod reaches its final velocity? Express the induced emf e with reference to vf using the Faraday’s law.
(c) (5 points) Find the value of the final velocity vf of the rod. What is the current through the resistance R when the rod reaches its final speed.
(d) (5 points) When the rod is sliding down with the final constant velocity vf, what is the amount of energy consumed by the resistance R in a unit time? Find the work done by the gravity on the rod in a unit time. Are they equal?
(e) (5 points) When the rod is sliding down with the final constant velocity vf, the resistance R is suddenly removed from the circuit. Describe the motion of the rod afterward.

PIC