# Homework Help: Magnetic field in radio lobes of cygnus (mainly just substition work)

1. Jan 7, 2009

### Brewer

1. The problem statement, all variables and given/known data
I have a radio map and radio spectrum of Cygnus A and have been asked to find the total energy of the source, the magnetic field in the lobes, the lifetime of the source and the average bulk power of the jets over the lifetime of the source. I've actually done all of this, apart from that the magnetic field bit requires me to use two different methods. I've used one method and got a value that appears acceptable (in that it makes all other value calculated with the number acceptable), but when working through with the other method (that I confirmed was a correct method with my lecturer) I get a value of about 10^38 T, obviously not in the acceptable range for Cygnus A (or anything ever as far as I know!).

This is due, I believe, to the constants in the equation, as the lecturer had stopped putting these in a few stages earlier and made some substitutions after this, leaving us with just a proportionality.

2. Relevant equations
So the equation I am attempting to use is:
$$B ~ \frac{\Theta^4 \nu^5}{(S_\nu)^2}$$ where $$\Theta$$ is the angular diameter in the sky of the object.

This comes from:
$$\frac{S_\nu c^2}{\Omega 2k\nu^2} = \frac{m_ec^2}{3k}(\frac{\nu}{\nu_g})^{\frac{1}{2}}$$

which can be rearranged to give an expression for the relativistic gyrofrequency in terms of the other variables. This is the last point at which there are constants in his derivation (and as a result in my notes too!)

From here I substituted in for the relativistic gyrofrequency with $$\nu_g = \frac{eB}{2\pi m_e}$$ and for the solid angle with $$\Omega = \frac{\pi}{4} \Theta^2$$, but are these correct things to substitue with? When I put my values in I get (as I said) a value of about 10^38 T which is clearly wrong. I think I'd be happier to find out that I was using the wrong substitutions that to find out that my basic algebra skills were wrong!

I hope I have provided enough information to try and help you help me, as my tex skills are pretty poor, but if you need any more information I will try and give it to you.

Any help is greatly appreciated!