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 0.10 s and delivers 7.7 x 10-6 J of energy perpendicularly to the 99-m2 surface area of the telescope's detector. The magnetar is thought to be 3.74 x 1020 m (about 40000 light-years) from earth, and to have a radius of 8.5 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 = 7.7*10-6 J The time taken for the pulse t = 0.1 s The surface area of the detector is A = 99 m2 The distance of the magnetar from earth is D = 3.74*1020 m The radius of the magnetar is R = 8.5*103 m The intensity of the pulse at the detector is                            I = E/At                            I = 7.7*10-6 J/(99 m2)(0.1 s)                             = 0.77*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(0.77*10-6 W/m2)/(376.64 )]                 Bmax = 8.03*10-11 T The rms magnetic field is             Brms = BmaxD/R2             Brms = (8.03*10-11 T)(3.74*1020 m)/(8.5*103 m)(2)             Brms = 2.5*106 T The energy delivered by the pulse is E = 7.7*10-6 J The time taken for the pulse t = 0.1 s The surface area of the detector is A = 99 m2 The distance of the magnetar from earth is D = 3.74*1020 m The radius of the magnetar is R = 8.5*103 m The intensity of the pulse at the detector is                            I = E/At                            I = 7.7*10-6 J/(99 m2)(0.1 s)                             = 0.77*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(0.77*10-6 W/m2)/(376.64 )]                 Bmax = 8.03*10-11 T The rms magnetic field is             Brms = BmaxD/R2             Brms = (8.03*10-11 T)(3.74*1020 m)/(8.5*103 m)(2)             Brms = 2.5*106 T The energy delivered by the pulse is E = 7.7*10-6 J The time taken for the pulse t = 0.1 s The surface area of the detector is A = 99 m2 The distance of the magnetar from earth is D = 3.74*1020 m The radius of the magnetar is R = 8.5*103 m The intensity of the pulse at the detector is                            I = E/At                            I = 7.7*10-6 J/(99 m2)(0.1 s)                             = 0.77*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(0.77*10-6 W/m2)/(376.64 )]                 Bmax = 8.03*10-11 T The rms magnetic field is             Brms = BmaxD/R2             Brms = (8.03*10-11 T)(3.74*1020 m)/(8.5*103 m)(2)             Brms = 2.5*106 T then                 Z = 376.64 The magnetic field is                Bmax = 0(2I/Z)                 Bmax = (4*10-7 H/m)[2(0.77*10-6 W/m2)/(376.64 )]                 Bmax = 8.03*10-11 T The rms magnetic field is             Brms = BmaxD/R2             Brms = (8.03*10-11 T)(3.74*1020 m)/(8.5*103 m)(2)             Brms = 2.5*106 T

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