A gamma-ray telescope intercepts a pulse of gamma radiation from a magnetar, a t

Question

A gamma-ray telescope intercepts a pulse of gamma radiation from a magnetar, a type of star with a spectacularly large magnetic field. The pulse lasts 0.14 s and delivers 9.5 x 10^-6 J of energy perpendicularly to the 57-m^2 surface area of the telescopes detector. The magnetar is thought to be 4.92 x 10^20 m (about 52000 light-years) from earth, and to have a radius of 7.2 x 10^3 m. Find the magnitude of the rms magnetic field of the gamma-ray pulse at the surface of the magnetar, assuming that the pulse radiates uniformly outward in all directions. (Assume a year is 365.25 days.)

Explanation / Answer

Intensity of radition at the telescope surface is 9.5X10^6 J/.14 s X57 m^2=11.9X10^5 J/s-m^2. The intensity is inversely proportional to square of radius of a point source and hence the intensity at magnetar is 11.9X10^5 X(4.92X10^20)^2/(7.2X10^3)^2=5.557X10^39 J/s-m^2. Intesity is directly proportional to square of rms magnetic field.

rms magnetic field = sqrt{2 X 4?

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