Ultra high energy cosmic ray deflection angle causes by magnetic field

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To determine the maximum angular deflection of an ultra-high energy cosmic ray with an energy of 10^20 eV from a source 10 Mpc away in a magnetic field of strength 10^-9 G, the Larmor radius is a key factor. The Larmor radius can be used to calculate the deflection angle, but initial attempts have not yielded reasonable results. A sketch of the particle's path alongside the calculations is recommended to visualize the problem. Clarification on the correct application of the Larmor radius and trigonometric principles is necessary for accurate results. Properly addressing these calculations will help in understanding the deflection angle.
Mikkel
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Homework Statement
Maximum angular deflection of proton influenced by B-field
Relevant Equations
Larmor radius: R = (c*p)/(Z*e*B)
I'm given an ultra-high energy cosmic ray with energy 10^20 eV. It is coming from a source 10 Mpc away with an extragalactic magnetic field with strength B = 10^-9 G. I am to determine the maximum angular deflection of this cosmic ray, so it hits Earth.

I don't have an attempt of the solution as I'm not even sure what formula to use. I was thinking of using the Larmor radius and using that as the distance the particle have traveled and then it is a trigonometric problem, but it doesn't give me a reasonable angle.

Any hits or thoughts are appreciated!
 
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You should use the Larmor radius to determine the deflection angle. Make a sketch of the path of the particle with your calculation of the defection angle and show us why it "doesn't give me a reasonable angle".
 
So is there some elegant way to do this or am I just supposed to follow my nose and sub the Taylor expansions for terms in the two boost matrices under the assumption ##v,w\ll 1##, then do three ugly matrix multiplications and get some horrifying kludge for ##R## and show that the product of ##R## and its transpose is the identity matrix with det(R)=1? Without loss of generality I made ##\mathbf{v}## point along the x-axis and since ##\mathbf{v}\cdot\mathbf{w} = 0## I set ##w_1 = 0## to...

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