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 0.16 s and delivers 9.2 x 10^-6 J of energy perpendicularly to the 78-m^2 surface area of the telescopes detector. The magnetar is thought to be 4.53 x 10^20 m (about 48000 light-years) from earth, and to have a radius of 7.5 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

given that time t = 0.16 s surface area A = 78 m2 energy E = 9.2 x10-6 J distance from the earth to the star x = 4.53 x 1020 m radius r = 7.5 x103 m speed of the light c = 3 x108 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 x 10-7 T.m/A substitute the given data in above equation , we get       Brms = (4.53x 1020 / 7.5x 103) [ 9.2 x10-6 (4 x10-7/78(0.16 s)(3x 108]1/2               = 3.35 x 106 T time t = 0.16 s surface area A = 78 m2 energy E = 9.2 x10-6 J distance from the earth to the star x = 4.53 x 1020 m radius r = 7.5 x103 m speed of the light c = 3 x108 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 x 10-7 T.m/A substitute the given data in above equation , we get       Brms = (4.53x 1020 / 7.5x 103) [ 9.2 x10-6 (4 x10-7/78(0.16 s)(3x 108]1/2               = 3.35 x 106 T time t = 0.16 s surface area A = 78 m2 energy E = 9.2 x10-6 J distance from the earth to the star x = 4.53 x 1020 m radius r = 7.5 x103 m speed of the light c = 3 x108 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 x 10-7 T.m/A substitute the given data in above equation , we get       Brms = (4.53x 1020 / 7.5x 103) [ 9.2 x10-6 (4 x10-7/78(0.16 s)(3x 108]1/2               = 3.35 x 106 T energy E = 9.2 x10-6 J distance from the earth to the star x = 4.53 x 1020 m radius r = 7.5 x103 m speed of the light c = 3 x108 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 x 10-7 T.m/A substitute the given data in above equation , we get       Brms = (4.53x 1020 / 7.5x 103) [ 9.2 x10-6 (4 x10-7/78(0.16 s)(3x 108]1/2               = 3.35 x 106 T

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