ps12

ps12 - 8.02 MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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

View Full Document Right Arrow Icon
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?
Background image of page 1

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

View Full DocumentRight Arrow Icon
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).
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/22/2009 for the course 8 02 taught by Professor Sciolla during the Fall '08 term at MIT.

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 Right Arrow Icon
Ask a homework question - tutors are online