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An electron and a proton are moving on straight parallel path with same velocity. They enter a region of semi infinite magnetic field perpendicular to velocity. What will happen there? Will both of them never come out of the field? Or they come out with same velocity at same time?

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    $\begingroup$ What do you think will happen? $\endgroup$ – Hritik Narayan Aug 30 '15 at 10:34
  • $\begingroup$ I do not know. It was asked in my exam. But I think there will be different possibilities. $\endgroup$ – Sulav Sigdel Aug 30 '15 at 10:36
  • $\begingroup$ Maybe this is a start: socratic.org/questions/… $\endgroup$ – user81619 Aug 30 '15 at 10:42
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    $\begingroup$ What generally happens to moving charges in a uniform magnetic field? (Where the field is perpendicular to their velocity?) $\endgroup$ – Hritik Narayan Aug 30 '15 at 10:43
  • $\begingroup$ Have a look at pa.msu.edu/courses/1997spring/PHY232/lectures/magforces/… $\endgroup$ – anna v Aug 30 '15 at 10:43
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Hint: A semi-infinite uniform magnetic field would be one which would be described by something like this: $B=0$ (for $x<0$) and $B=constant$ (for $x\ge0$).

The question describes a situation of this sort: (The $X$s indicate that the region has a magnetic field directed into/out of the page):

enter image description here

You need to know how the trajectory of a charged particle is going to be in a uniform field region. (This trajectory would describe the particles motion only when the particle is in the region where the field is present.)

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The electron will turn to one side and the proton will turn to the other side. Say, the electron will describe a spiral path to the left (this depends from the direction of the magnetic field), then the proton will describe a spiral path to the right. This happens because both particles have a magnetic dipole moment and an intrinsic spin. Aligning the magnetic dipole moments the spins get deflected. Due to the gyroscopic effect this is the reason for the spirale path of both elements. But why the get deflected to different directions? Say, the magnetic dipole moment and the intrinsic spin of the electron oriented parallel. Then this parameters for the proton oriented anti-parallel.

The spirale paths are from different curvature. The electrons spirale is more bended then the protons. This is because they have the different masses.

Last not least why they move in spirale paths and not in a circle. This is because both particles emit photons when get deflected. Photons have momentum and this momentum they get from the particles which loose this moment and move slower and slower until they stop.

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  • $\begingroup$ The answer is correct, but most questions at that level neglect the fact that accelerating charges radiate! Don't you think this makes it too complicated for the OP? (Also, the handedness of the trajectory can simply be explained by the charge difference!) $\endgroup$ – Hritik Narayan Aug 30 '15 at 11:17
  • $\begingroup$ @HritikNarayan: The photons emission is an essential part of the full picture about particle deflection in magnetic field. Without this emission the deflection will stop after alignment of the electrons magnetic dipole moment. This really happens if the electron is not moving and an external magnetic field is switched on. $\endgroup$ – HolgerFiedler Aug 30 '15 at 12:01
  • $\begingroup$ @HritikNarayan: The electric charge is not influencable by a magnetic field. The magnetic dipole moment of charged particles is interacting with the external magnetic field. Bay the way, a neutron is influenced by a magnetic field too. $\endgroup$ – HolgerFiedler Aug 30 '15 at 12:05
  • $\begingroup$ I'm aware, but at that level, they're taught that $F_{mag}=q(v \times B)$. The direction of the changes with the sign of $q$! $\endgroup$ – Hritik Narayan Aug 30 '15 at 13:23
  • $\begingroup$ @HritikNarayan Agree with you. There are a lot of such questions in the forum and it seems, that the teaching level stops at the Lorentz force. The nature of electromagnetic induction (Lorentz force, electric induction, magnetic induction) is not exposed well. How about my paper? $\endgroup$ – HolgerFiedler Aug 30 '15 at 13:45

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