An astronomer detects a signal of 2480 MHz from an electron travelling in a distant nebula. What is the strength of the magnetic field in the nebula?
When a charged particle q enters with a speed v, in a uniform magnetic field B, experiences a magnetic force given by:
Fm = q (v x B)
Assuming that the velocity is perpendicular to the field; the magnetic force acts as a centripetal force and the electric charge makes a circular motion. Thus we can write:
Fc = Fm = mac
m → is the mass of the charged particle.
ac → is the centripetal acceleration.
Substituting the expressions for the magnetic force and centripetal acceleration, we have:
qvB = mv^2/r
r → is the radius of the circular path.
From the above equation, the speed v is:
v = rqB/m
The angular frequency of the circular motion is expressed as:
w = 2πf = v/r
In this case, this frequency is called, "cyclotron frequency".
2πf = qB/m → B = 2πfm/q
Substituting the values, we have:
B = (6.28)(2.48 x 10^9)(9.109 x 10^-31)/(1.602 x 10^-19)
B = 88.55 x 10^-3 T