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 0.23 s and delivers 8.00 x 10 - 6 J of energy perpendicularly to the 68-m2 surface area of the telescope's detector. The magnetar is thought to be .50 x 10 20 m (about 50 000 light-years) from earth, and to have a radius of 8.60 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.

Explanation / Answer

The energy delivered by the pulse is E = 8*10-6 J The time taken for the pulse t = 0.23 s The surface area of the detector is A = 68 m2 The distance of the magnetar from earth is D = 4.5*1020 m The radius of the magnetar is R = 8.6*103 m The intensity of the pulse at the detector is I = E/At I = 8*10-6 J/(68 m2)(0.23 s) = 0.5115*10-6 W/m2 The impedence of the free space is Z = ?(?0/?0) Where ?0 = 4?*10-7 H/m and ?0 = 8.854*10-12 C2/Nm2 , then Z = 376.64 ? The magnetic field is Bmax = ?0?(2I/Z) Bmax = (4?*10-7 H/m)?[2(0.5115*10-6 W/m2)/(376.64 ?)] Bmax = 6.5458227e-11 T The rms magnetic field is Brms = BmaxD/R?2 Brms = (6.5458227e-11 T)(4.5*1020 m)/(8.6*103 m)(?2) Brms = 2.422305*106 T then Z = 376.64 ? The magnetic field is Bmax = ?0?(2I/Z) Bmax = (4?*10-7 H/m)?[2(0.5115*10-6 W/m2)/(376.64 ?)] Bmax = 6.5458227e-11 T The rms magnetic field is Brms = BmaxD/R?2 Brms = (6.5458227e-11 T)(4.5*1020 m)/(8.6*103 m)(?2) Brms = 2.422305*106 T

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