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I have been trying to answer part b) of the question below: enter image description here

(The image is the image of the cyclotron in question)

To find the direction of the magnetic field acting on the protons I tried using the right hand rule, treating the direction of current as "upwards" and the force on the protons as "to the left", which gives me the answer "in to the page". This is the right answer, however I am uncertain as to whether by method of finding it is correct. So, I am wondering if my method is indeed correct or not.

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Your reasoning is correct: you're using the equation for the Lorentz force $\vec{F} = q\vec{v}\times\vec{B}$ where you know the direction of the force and the current.

What may be a little confusing about your approach is that you're applying the Lorentz force formula at the point where the proton has already been deflected a bit, and is travelling upwards (with the force pointing to the left). Try applying it for the moment where the proton is just entering the D (what are the directions of $\vec{v}$ and $\vec{F}$ here?).

The result will of course be the same, but it will help you understand where the initial deflection comes from.

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