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 0.32 s and delivers 6.5 × 10-6 J of energy perpendicularly to the 57-m2 surface area of the telescope's detector. The magnetar is thought to be 3.52 × 1020 m (about 37000 light-years) from earth, and to have a radius of 7.7 × 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

Intensity at the surface of the earth, I = Power/Area

= (6.5*10^-6/0.32)/57

= 3.56*10^-7 W/m^2

let r1 = 3.52*10^20 m

r2 = 7.7*10^3 m

I1 = 3.56*10^-7 W/m^2

Let I2 is the intensity at the surface of the magnetar.

use,

I2/I1 = r1^2/r2^2

I2 = I1*(r1/r2)^2

= 3.56*10^-7*(3.52*10^20/(7.7*10^3))^2

= 7.44*10^26 W/m^2

we know, Brms = sqrt(I*mue/c)

= sqrt(7.44*10^26*4*pi*10^-7/(3*10^8))

= 1.76*10^6 T <<<<<<<----------------------Answer

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