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.