ps12

# ps12 - 8.02 MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

This preview shows pages 1–3. Sign up to view the full content.

PS12-1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2008 Label with your name, table number and group. Turn in at the homework box. Problem Set 12 Due: Tuesday, December 2 nd at 11:30 am Analytic Problems… Problem 1: Coaxial Cable and Power Flow A coaxial cable consists of two concentric long hollow cylinders of zero resistance; the inner has radius a , the outer has radius b , and the length of both is l , with l >> b , as shown in the figure. The cable transmits DC power from a battery to a load. The battery provides an electromotive force ε between the two conductors at one end of the cable, and the load is a resistance R connected between the two conductors at the other end of the cable. A current I flows down the inner conductor and back up the outer one. The battery charges the inner conductor to a charge Q and the outer conductor to a charge Q + . (a) Find the direction and magnitude of the electric field E G everywhere. (b) Find the direction and magnitude of the magnetic field B G everywhere. (c) Calculate the Poynting vector S G in the cable. (d) By integrating S G over appropriate surface, find the power that flows into the coaxial cable. (e) How does your result in (d) compare to the power dissipated in the resistor? Problem 2: Electromagnetic Plane Wave An electromagnetic plane wave is propagating in vacuum has a magnetic field given by 0 10 1 ˆ () ( ) 0 u B f ax bt f u else < < =+ = Bj G The wave encounters an infinite, dielectric sheet at x = 0 of such a thickness that half of the energy of the wave is reflected and the other half is transmitted and emerges on the far side of the sheet. (a) What condition between a and b must be met in order for this wave to satisfy Maxwell’s equations?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
PS12-2 (b) What is the magnitude and direction of the E G field of the incoming wave? (c) What is the magnitude and direction of the energy flux (power per unit area) carried by the incoming wave, in terms of B 0 and universal quantities? (d) What is the pressure (force per unit area) that this wave exerts on the sheet while it is impinging on it? Problem 3: Formation of a Standing Wave Two waves traveling in opposite directions produce a standing wave, as discussed in Section 13.5 of the Course Notes . Let the individual wave functions be 12 (5.0 cm)sin(3.0 2.0 ), (5.0 cm)sin(3.0 2.0 ) yx t t =− =+ where x and y are measured in centimeters. (a) By applying superposition principle, find the resultant wave function. (b) What is the amplitude of the resultant simple harmonic motion at 3.0 cm x = ? (c) Find the positions of the nodes (the points of zero amplitude) and the antinodes (the maximum amplitude points).
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 13

ps12 - 8.02 MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online