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 0.13 s and delivers 8.6 x 10-6 J of energy perpendicularly to the 70-m2 surface area of the telescope's detector. The magnetar is thought to be 3.95 x 1020 m (about 42000 light-years) from earth, and to have a radius of 7.4 x 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. (Assume a year is 365.25 days.)

Explanation / Answer

The energy delivered by the pulse is E = 8.6*10-6 J The time that the pulse lasts is t = 0.13 s The surface area of the detector is A = 70 m2 The distance of the magnetar is D = 3.95*1020 m The radius of the magnetar is R = 7.4*103 m The intensity of the pulse at the detector is I = E/At I = 8.6*10-6 J/(70 m2)(0.13 s) = 1.35*10-8 W/m2 The impedence of the free space is Z = (0/0) Where 0 = 4*10-7 H/m is the permiability of free space 0 = 8.854*10-12 C2/Nm2 is the permitivity of free space Z = 376.64 The magnetic field is Bmax = 0(2I/Z) Bmax = (4*10-7 H/m)[2(1.35*10-8 W/m2)/(376.64 )] Bmax = 1.064*10-11 T The RMS magnetic field is BRMS = BmaxD/R2 BRMS = (1.064*10-11 T)(3.95*1020 m)/(7.4*103 m)(2)
BRMS = 4.015*105 T The energy delivered by the pulse is E = 8.6*10-6 J The time that the pulse lasts is t = 0.13 s The surface area of the detector is A = 70 m2 The distance of the magnetar is D = 3.95*1020 m The radius of the magnetar is R = 7.4*103 m The intensity of the pulse at the detector is I = E/At I = 8.6*10-6 J/(70 m2)(0.13 s) = 1.35*10-8 W/m2 The impedence of the free space is Z = (0/0) Where 0 = 4*10-7 H/m is the permiability of free space 0 = 8.854*10-12 C2/Nm2 is the permitivity of free space Z = 376.64 The magnetic field is Bmax = 0(2I/Z) Bmax = (4*10-7 H/m)[2(1.35*10-8 W/m2)/(376.64 )] Bmax = 1.064*10-11 T The RMS magnetic field is BRMS = BmaxD/R2 BRMS = (1.064*10-11 T)(3.95*1020 m)/(7.4*103 m)(2)
BRMS = 4.015*105 T

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