where M is the magnetic dipole moment, is the anglebetween rotational axis and m
ID: 1752623 • Letter: W
Question
where M is the magnetic dipole moment, is the anglebetween rotational axis and magnetic dipole moment and isthe spin angular velocity. Show the spin angular velocity obeys thefollowing equation. Calculate the proportional constant k and the braking index nfor pure dipole radiation.Explanation / Answer
write the energy loss equation as dE/dt = -4 >>> =2M2sin2/3c3 a) the magnetic dipole radiation extracts rotational energy fromthe neutron star. rotational energy = (1/2) I 2 >>> Iis the moment of inertia dE/dt = d/dt ((1/2) I 2 ) = I(d/dt)= -4 d/dt = - (/I)3 =-kn So, k = /I = 2M2sin2/3Ic3, braking index n = 3 b) If d/dt = -kn d2/dt2 =-knn-1d/dt (d2/dt2) / (d/dt) =-knn-1= n(d/dt)/ n = (d2/dt2) /(d/dt)2 c) to estimate age of the neutron star, start with d/dt = -k3 assuming braking index stays constant at 3, we can integrate thisby rewriting d/3 = -kdt integrating from t=0 to t= tage , -(1/2)(1/2 - 1/02) =-ktage >>> is the currentspin velocity; what you call now since >> you have to use P = 2/ hope this helps!Related Questions
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