- #1

Norman

- 897

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I am studying for my qualifier and doing problems out of Jackson.

I am stuck on this one... any help would really be appreciated... I am unsure how to begin:

Jackson 7.15

The partially ionized interstellar medium (mostly hydrogen) responds to optical frequencies as an electronic plasma in a weak magnetic field. The broad-spectrum pulses from a pulsar allow determination of some average properties of the interstellar medium. The treatment of an electronic plasma in a magnetic field of Section 7.6 is pertinent.

a) Ignoring the weak magnetic field and assuming that [itex] max(w_p) \ll w [/itex], show that c times the transit time of a pulse of mean frequency w from a pulsar a distance R away is

[tex] ct(w) \approx R+\frac{e^2}{2 \epsilon_0 m_e w^2} \int n_e (z) dz [/tex]

where [itex] n_e (z) [/itex] is the electron density along the path of light.

so this is what I have so far:

ignoring the weak B-field the position has a solution of:

[tex] x=\frac{e}{m_e w^2}E [/tex]

and obviously ct(w) is a distance, but now I am lost...

Please help, I have been stumbling with this problem for a couple of days and it is turning into a monster that I need to solve.

Thanks for any help you can give.

(ps. I have read the pertinent section of Jackson over and over... I don't see any help in it.)