PHYSICS DEPARTMENT COLLEGE OF NEW YORK

PHYSICS 208EE FINAL EXAM DEC. 20, 2004 10:35 AM 140 MINUTES

A single double-sided 8.5 x 11 sheet of paper with notes is allowed. All work must be shown in the accompanying blue book.

Problem 1. A transverse sinusoidal wave with an amplitude of 2.50 mm and a wavelength of 1.80 m travels from left to right along a long, horizontal stretched string with a speed of 36.0 m/s. The origin is at the left end of the undisturbed string. At time t = 0 the left end of the string has its maximum upward displacement

(a) What are the frequency, angular frequency, and wave number of the wave? (b) What is the function y(x,t) that describes the wave? (c) What is y(t) for a particle at the left end of the string? (d) What is y(t) for a particle 1.35 m to the right of the origin? (e) What is the maximum magnitude of transverse velocity of any particle of the string? (f) Find the transverse displacement and the transverse velocity of a particle 1.35 m to the right of the origin at time t = 0.0625 s.

Problem 2. Two positive point charges q are placed on the y-axis at y = a and y = -a. A negative point charge -Q is located at some point on the +x-axis.

(a) In a free-body diagram, show the forces that act on the charge -Q. (b) Find the x- and y-components of the net force that the positive charges exert on -Q. (c) What is the net force on the charge -Q when it is at the origin (x = 0)? (d) Graph the x-component of the net force on the charge -Q as a function of x for values of x between -4a and +4a. Problem 3. A uniformly charged ring has radius a = 15.0 cm and has total charge of q = +24 nC. An electron (e = 1.6 x 10-19 C, me = 9.11 x 10-31 kg) is placed on the ring's axis a distance x = 30.0 cm from the center of the ring and is constrained to stay on the axis of the ring. The electron is then released from rest.

q

x

a (a) Find the electric potential of the ring on its axis as a function of x. (b) Describe the motion of the electron after its release. (c) Find the speed of the electron wh en it reaches the center of the ring.

Problem 4. An electrical conductor designed to carry large currents has a circular cross section 2.50 mm in diameter and is 14.0 m long. The resistance between its ends is .104 ohms.

(a) What is the resistivity of the material? (b) If the electric field magnitude in the conductor is 1.28 V/m, what is the total current? (c) If the material has 8.5 x 1028 free electrons per cubic meter, find the average drift speed under the conditions of part (b) (d) How much energy is dissipated in the conductor in 1 minute?

Problem 5. The plane of a 5.0 cm x 8.0 cm rectangular loop of wire is parallel to a 0.19 T magnetic field. The loop carries a current of 6.2 A.

(a) What torque acts on the loop? (b) What is the magnetic moment of the loop? (c) What is magnetic flux through the loop? (d) For what orientation of the coil is the magnitude of the torque 71 % of that found in part {a)? (e) What is the magnetic flux through the loop in part (d)?

Problem 6. The current in the long straight wire AB is upward and increasing steadily at the rate di/dt = 9.60 A/s. At t = 0, the current is 0 amperes.

(a) Write down an expression for the current i(t) as a function of time. (b) Find the magnetic field B(r) as a function of the distance from the wire r. (c) At the instant when i = 1 A, what is the flux through the loop? (d) What is the induced emf in the loop?

b

La

i

Problem 7. In an RLC circuit, R = 400 ohms, L = 0.350 H, and C = 0.0120 mF. (a) What is the resonance angular frequency of the circuit? (b) The capacitor can withstand a peak voltage of 550V. What is the maximum current amplitude?

(c) What is the maximum source voltage amplitude?

Problem 8. Your camera lens has a convex lens with a 35.0 mm focal length and film that is 36.0 mm wide. In taking a picture of an airplane 22.7 m in length you find that the image of the airplane fills only 3/4 of the width of the film.

(a) How far are you from the airplane? (b) How close should you stand if you want to fill the width of the film with the airplane's image?

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