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 0.33 s and delivers 6.0 × 10^-6 J of energy perpendicularly to the 70-m^2 surface area of the telescope's detector. The magnetar is thought to be 5.24 × 10^20 m (about 55000 light-years) from earth, and to have a radius of 8.2 × 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.)
time t = 0.33 s
surface area A = 70 m2
energy E = 6*10^-6 J
distance from the earth to the star x = 5.24*10^20 m
radius r = 8.2*10^3 m
speed of the light c = 3*10^8 m/s
the magnitude of the rms magnetic field of the
gamma-ray pulse at the surface of the magnetar is
Brms = (x/r)
[Eμ0/Atc]1/2 ............ (1)
where , permeability μ0
= 4π*10-7 T.m/A
substitute the given data in above equation , we get
Brms = (5.24*10^20 / 8.2*10^3) [
6*10^-6*4π*10^-7/70*0.33*3*10^8]1/2
= 2.10*10^6 T
A gamma-ray telescope intercepts a pulse of gamma radiation from a magnetar, a type of star...