# hmwk7 - It is observed that iF a pulse is detected at...

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Homework set 12 November 9, 2001 1. Jackson problem 7.3. Please show a detailed calculation including all necessary steps. 2. Jackson problem 7.5. Please show a detailed calculation including all necessary steps. 3. (A). Consider two electromagnetic plane waves propagating in a dispersive medium. The frst wave has Frequency ω and wavenumber k , while the second wave has Frequency ω + Δ ω and wavenumber k k . At time t there are points in space where the two waves are in phase, producing an interFerence maximum. Show that, For Δ k 0, the velocity oF these points is V g = dk V g is the group velocity. Sketch V g and the pahse velocity V p as a Function oF ω For a collisionless plasma. ±ind V g in terms oF V p For such a medium. (B). A rotating neutron star emits radio pulses oF duration 5–50 msec at intervals oF 1 sec. These pulses propagate through the interstellar medium oF ionized hydrogen.

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Unformatted text preview: It is observed that iF a pulse is detected at Frequency ω at time t , a pulse at Frequency ω + Δ ω will be detected at time t + Δ t . ±ind the relation between Δ t , Δ ω , and the dispersive measure DM = Z L n e dl, where L is the distance to a neutron star, n e is the electron number density, and dl an element oF path length along the line oF sight. Discuss the sign oF Δ t/ Δ ω . (C). Consider the Following data For the neutron star PSR 0950 + 08: THe average density Fo 1 electrons in the solar neighborhood is 0 . 03 cm-3 . Find the distance to PSR 0950 + 08. (D). The observed dispersion in the data for PSR 0950 + 08 could be due in part to the photon having a ±nite mass. Find an upper limit to the mass of the photon. 4. Jackson problem 7.14. 5. Jackson problem 7.19. 2...
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hmwk7 - It is observed that iF a pulse is detected at...

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