# Equation of motion of charged particle under effect of magnetic field

A charged particle with specific charge q/m diverges from the origin [to the first quadrant] by angle X with x axis and with velocity v. To bring the particle back to the x axis, a magnetic field B is applied along positive x axis from the origin. What will be the equation of motion of the particle?

My approach to the problem is given below.

I believe that the curve should be like this:

Now since in the problem the electric field is zero according to Lorentz Law the force acting on the particle should be $q(vXB) = q \cdot v \cdot B \cdot \sin(X_t)$, where $X_t$ is the angle the velocity of the particle makes with the X axis at a particular moment. Now where I am stuck is that $X_t$ is not constant. You can see from the curve that the angle the tangent to the curve makes with the x axis is not constant, it changes. It would be very helpful if someone helps me or at least gives me a hint how can I relate $X_t$ with $x$, which is the horizontal distance traveled. That way I will know the value of $dy/dx$ for some $x$, after which I can integrate to get my answer.

Thanks.

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Hi man. Welcome to Physics.SE. This site deals with conceptual Physics Q&A. We don't encourage homework questions that doesn't involve any sort of work done by the author (which is you) and asks other users to solve the problem. If you think you could clarify your question, add what you've done along with your question. We're ready to help you. If you aren't clear, Please have a look at our homework policy for more info. After improving the post, flag it for moderator attention. –  Waffle's Crazy Peanut Apr 17 '13 at 16:41
Ok, I am writing my approach in the next comment. –  man Apr 17 '13 at 16:42
No, please don't fill-up the comment space. You can always include it in your post ;-) –  Waffle's Crazy Peanut Apr 17 '13 at 16:43
Okay, I am editing it to my post. @Crazy Buddy Thanks for the tip. –  man Apr 17 '13 at 16:45