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 8.60*10^-6 J of energy perpendicularly to the 74-m2 surface area of the telescope's detector. The magnetar is thought to be 4.50*10^20 m (about 50000 light-years) from earth, and to have a radius of 8.70*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.
Answer in Tesla

Explanation / Answer

Given energy delivered by the magnetor e = 8.6*10-6 J time    t = 0.25 s radius of magnetor r = 8.7*10 3 m       the relation between intesity and electricifeld is                          I   = E max2   / 2 o c                P / 4r 2   =   E max2   / 2 o c                       E max2   = P o c / 2r 2                                  = e o c / 2r 2 .t                                = ( 8.6*10-6 ) ( 4*10-7 ) ( 3*108 ) / 2( 8..7*103) . 0.25                                 = 0.2372                             Emax = 0.4870 N/C    the relation between electricfield and magneticfield                   E max / B max = c        maximum magneticfield is                      B max = E max / c                                  = 0.4870 / ( 3*10 8 m/s )                                   = 1.623*10-9 T                Brms   = B max / 2                           = 1.623*10-9 / 1.414                            = 1.148 nT time    t = 0.25 s radius of magnetor r = 8.7*10 3 m       the relation between intesity and electricifeld is                          I   = E max2   / 2 o c                P / 4r 2   =   E max2   / 2 o c                       E max2   = P o c / 2r 2                                  = e o c / 2r 2 .t                                = ( 8.6*10-6 ) ( 4*10-7 ) ( 3*108 ) / 2( 8..7*103) . 0.25                                 = 0.2372                             Emax = 0.4870 N/C    the relation between electricfield and magneticfield                   E max / B max = c        maximum magneticfield is                      B max = E max / c                                  = 0.4870 / ( 3*10 8 m/s )                                   = 1.623*10-9 T                Brms   = B max / 2                           = 1.623*10-9 / 1.414                            = 1.148 nT

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