Can a CHANGING magnetic field change the speed of a charged particle

  1. We had this ques. in a test - "can a changing magnetic field change the speed of a charged particle". The ans given to us was "no because it's velocity is perpendicular to the magnetic force due to the mag field" but a friend of mine wrote that a changing mag. field will induce an emf which will act on the particle and change its speed and hence the mag field can change the speed.
    I can not prove him wrong and so i think he is right.
    What's going on here
  2. jcsd
  3. ZapperZ

    ZapperZ 29,752
    Staff Emeritus
    Science Advisor
    Gold Member

    First of all, the question is a bit vague. When we talk about something "changing", it must be changing with respect to a particular variable. In this case, is the magnetic field changing with position (which means that it has a gradient over distance), or is it changing with respect to time (which means that it is time varying)?

    For the latter, one can easily invoke one of Maxwell's equation, which is Faraday's law that says that a time-varying magnetic field can induce an electric field (more accurately, the curl of the electric field is not zero). And we all know that the presence of an electric field can change the speed of a charged particle.

  4. So for the case you considered my friend is right?
    And will it not be the same if the field was changing with position.
  5. jtbell

    Staff: Mentor

    Yes. This is the principle behind an early type of particle accelerator, the betatron:
  6. No, if the field is changing with position, but not with time, there is no induced electric field.
  7. It's also ambiguous in the sense that, even in the case of a time-varying magnetic field, one can argue that it is not the time varying magnetic field which is changing the speed of the particle, it is the electric field.
  8. thanks,
    sorry for that stupid ques about mag field changing with position...
    i dont know why i asked that?
  9. Drakkith

    Staff: Mentor

    I was under the impression that a magnetic field changes in both position and time. How else would moving a magnet in and out of a coil produce a current?
  10. Well, of course it can! This happens all the time in a loop of conducting wire rotating in a magnetic field, such as in that of a dynamo or other electrical generator.

    The electron is a charged particle. As the loop rotates, the direction of the magnetic field through the loop changes. This generates an AC current in the wire. The speed of the electrons in the wire change from zero to plus or minus a voltage that depends on the strength of the changing magnetic field.

    How could it be that no one else here gets this, or am I missing some nuance of the question?
  11. WannabeNewton

    WannabeNewton 5,767
    Science Advisor

    A magnetic field can change in time or position or both but there is no reason it must necessarily change in both. If the magnetic field has time variation then it will "generate" a current. Spatial variation doesn't matter for that.
  12. Matterwave

    Matterwave 3,816
    Science Advisor
    Gold Member

    You are correct. A static (in time) magnetic field can also induce an EMF if the area in Faraday's law is changing with respect to the magnetic field. This is because to a particle in motion relative to a magnetic field, even if the magnetic field is static, the Lorentz transformation to a moving frame of reference will produce an electric field.

    In the moving frame of the moving particle (moving current loop), there IS an electric field and an induced emf.
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