This is a question from Bangladesh Physics Olympiad:


Draw the trajectory of the charge $+q$ .Necessary informations are given in the figure. $B$ is the magnetic field.

What I want to know is whether there is enough information to get the parametric equation for $x, y$ - co-ordinates or not?

So far, I have been only able to roughly draw the trajectory. As the instantneous radius for a moving charged particle $r=\frac{mv}{qB}$ and the instantneous velocity of the particle is going to increase always due to gravity; the instantneous radius of the trajectory will increase. So, the curvature of trajectory will decrease in time.

But, I want to work out the parametric equation for the trajectory. But I don't know how to. Any hints?


closed as off-topic by John Rennie, sammy gerbil, Jon Custer, M. Enns, David Hammen Aug 1 '17 at 0:41

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  • 3
    $\begingroup$ This is a standard crossed electric and magnetic field problem in disguise. The constant force due to the electric field on a charged particle being replaced by the constant force due a gravitational field. Have a look at physics.stackexchange.com/a/337968/104696 So in a roundabout way this is really a duplicate? $\endgroup$ – Farcher Jul 31 '17 at 5:52
  • $\begingroup$ Hi Mockingbird. I'm afraid this runs afoul of our homework and exercises policy (or at least the exercises bit of it). The vertical motion is just the usual motion under gravity and the horizontal motion is due to the Lorentz force. $\endgroup$ – John Rennie Jul 31 '17 at 5:58
  • $\begingroup$ @John Rennie Are yous sure about it $\endgroup$ – Mockingbird Jul 31 '17 at 6:39
  • $\begingroup$ @Mockingbird Yes $\endgroup$ – John Rennie Jul 31 '17 at 7:07
  • $\begingroup$ I agree with John Rennie : you are asking us to show you how to solve a problem, rather than asking about a conceptual difficulty which you have encountered. This makes your question off topic. ... I agree with Farcher about the shape of the trajectory. $\endgroup$ – sammy gerbil Jul 31 '17 at 10:53