Answer
$F = (-7.75\times 10^{-23}~N)~\hat{i}$
Work Step by Step
We can find the magnetic field at the proton's position due to the current:
$B = \frac{\mu_0~i}{2~\pi~R}$
$B = \frac{(4\pi\times 10^{-7}~H/m)(0.350~A)}{(2~\pi)~(0.0289~m)}$
$B = 2.422\times 10^{-6}~T$
By the right hand rule, the magnetic field is in the +z direction.
We can find the magnetic force on the proton:
$F = qv\times B$
$F = (1.6\times 10^{-19}~C)(-200~m/s~\hat{j})\times (2.422\times 10^{-6}~T~\hat{k})$
$F = (-7.75\times 10^{-23}~N)~\hat{i}$
