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?

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