Radio astronomers detect electromagnetic radiation at a frequency of 42MHz from an interstellar gas cloud. If the radiation results from electrons spiraling in a magnetic field, What is the magnetic field strength inside the gas cloud?

Explanation:

The electrons will also spiral with frequency of 42 x 10⁶

n = 42 x 10⁶

For circular motion of electron

= Bqv = m ω² r ( centripetal force )

v / r = m ω² / Bq

= 4π² n² m / Bq

T =  2πr / v

1 / n  = 2πr / v

r / v = 1 / 2π n

2π n = ω²m / Bq

ω = ω² m/ Bq

B =  ω m / q

B = 2π nm / q

= 2  x 3.14 x 42 x 10⁶ x 9.1 x 10⁻³¹ / 1.6 x 10⁻¹⁹

= 15 x 10⁻⁴  T

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