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Test charge in electric and magnetic field

  1. Apr 30, 2013 #1
    Consider an proton placed at the origin; a uniform electric field exists along the Y axis, and a uniform magnetic field along the Z axis. In what direction does the proton accelerate? My intuition is that it accelerates along the X axis, normal to both fields, but I'm not sure. Can anyone derive a solution?
  2. jcsd
  3. Apr 30, 2013 #2


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    Staff: Mentor

    "Placed at the origin" implies to me that the proton is initially at rest.

    In what directions are the initial electric, magnetic and net forces on the proton?

    What happens after the proton starts to move (how do the forces change)?
  4. Apr 30, 2013 #3
    Well initially velocity is zero, so the magnetic force is also zero. But as soon as it starts moving, the magnetic force is nonzero, so I'm not sure. I guess it should initially accelerate in the direction of the E field, then turn along the X axis.

    Edit: To clarify, Force due to the E field will always be down(-Y), and Magnetic Force will be orthogonal to both B and V, as per the RHR
    Additionally, because the B field can't do work, the charge can never move above the X axis, and velocity will be a function of it's Y position.

    And... I guess I answered my own question. There will be an asymtote such that Magnetic force is equal and opposite electric force, and the charge stops accelerating, with velocity along the X axis, and a negative Y position.
    Last edited: Apr 30, 2013
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