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 0.25 s and delivers 7.80 10-6 J of energy perpendicularly to the 77-m2 surface area of the telescope's detector. The magnetar is thought to be 4.50 1020 m (about 50 000 light-years) from earth, and to have a radius of 8.10 103 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.
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Explanation / Answer

time t = 0.25 s surface area A = 77 m2 energy E = 7.8*10-6 J distance from the earth to the star x = 4.5*1020 m radius r = 8.1*103 m speed of the light c = 3*108 m/s the magnitude of the rms magnetic field of the gamma-ray pulse at the surface of the magnetar is       Brms = (x/r) [E0/Atc]1/2     ............ (1)         where , permeability 0 = 4*10-7 T.m/A substitute the given data in above equation , we get       Brms = (4.5*1020 / 8.1*103) [ 7.8*10-6*4*10-7/77*0.25*3*108]1/2               = 2.28*106 T energy E = 7.8*10-6 J distance from the earth to the star x = 4.5*1020 m radius r = 8.1*103 m speed of the light c = 3*108 m/s the magnitude of the rms magnetic field of the gamma-ray pulse at the surface of the magnetar is       Brms = (x/r) [E0/Atc]1/2     ............ (1)         where , permeability 0 = 4*10-7 T.m/A substitute the given data in above equation , we get       Brms = (4.5*1020 / 8.1*103) [ 7.8*10-6*4*10-7/77*0.25*3*108]1/2               = 2.28*106 T

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