OK first off here is the problem.(adsbygoogle = window.adsbygoogle || []).push({});

problem:A positive point charge q of mass m is injected with a velocity [tex]u_0 = \mu_0 j[/tex] into the y > 0 region where a uniform magnetic field [tex]B = B_0 i[/tex] exists. Obtain the equation of motion of the charge, and describe the path that the charge follows.

i, j and k represent unit vectors in the direction of the x, y and z axes.

Now I understand that the path will be a semicircle from the theory of the motion of a charged particle in a uniform magnetic field and since y > 0 and I know that the force experienced by the particle will be in the z direction.

[tex]F_m = q(u_0 X B) = q \mu_0 B_0 k[/tex]

The velocity is going to be constant, but the motion will vary with time in the z direction I think? Obviously my problem is that I'm not too sure of how to solve for the equation of motion in this problem. I guess one of the reasons why I'm finding this so difficult is I can't even visualise it properly.

Any help to put me on the right track would be great.

Thanks

EDIT: I can get the answer by simply equating the centripetal and magnetic forces and then substituting [tex]R= \frac {m \mu_0} {q B_0}[/tex] into the general equation of a semicircle, but I don't think this is how they want you to do it.

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# Motion of charged particle in a magnetic field

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