As the outer layers of the Supernova star explode outwards, its innermost core c

Question

As the outer layers of the Supernova star explode outwards, its innermost core collapses from a radius of 3.3 X 106 m down to 14000 m. The core will become a neutron star.

a) If the angular momentum of the core is conserved, by what factor must the angular speed increase, and if the initial- peak-magnetic-field of the core is 8300 T what will be the peak-magnetic-field of the neutron star after the collapse?

b) Why exactly would such a rotating object have a magnetic field, and where is the current that produces the magnetic field?

Explanation / Answer

R1 = initial radius = 3.3 X 106 m

R2 = final radius = 1.4 x 104 m

let the mass of star be ''m''

then initial moment of inertia, I1 = 2/5 m R12

final moment of inertia , I2 = 2/5 m R22

W1 = initial angular speed

W2 = final angular speed

Using conservation of angular momentum

I1 W1 = I2 W2

(2/5 m R12 ) W1 = (2/5 m R22) W2

(3.3 X 106)2W1 = (1.4 x 104)2W2

(5.56 x 104 ) W1 = W2

angular speed becomes (5.56 x 104 ) times

magnetic field is inversly propotional to the radius

so   B1 /B2 = R2 /R1

8300 /B2 = 14000/(3.3 x 106)

B2 = 1.96 x 106

b)    the core of the star has charge . when this charge moves in circular path , it behaves as a current. which produces the magnetic field.

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