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

In summary: So, yes, a static magnetic field can induce an emf by changing its position. Zz.In summary, the question is whether a changing magnetic field can change the speed of a charged particle. The answer given was no, due to the perpendicular velocity to the magnetic force. However, a friend argues that a changing magnetic field can induce an emf, which can change the speed of the particle. This is possible because a time-varying magnetic field can generate an electric field, which can affect the speed of the charged particle. It is also possible for a static magnetic field to change the speed of a particle by changing its position.
  • #1
aniket7tomar
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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
 
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  • #2
aniket7tomar said:
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

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.

Zz.
 
  • #3
So for the case you considered my friend is right?
And will it not be the same if the field was changing with position.
 
  • #4
aniket7tomar said:
So for the case you considered [time-varying magnetic field] my friend is right?

Yes. This is the principle behind an early type of particle accelerator, the betatron:

http://en.wikipedia.org/wiki/Betatron
 
  • #5
aniket7tomar said:
So for the case you considered my friend is right?
And will it not be the same if the field was changing with position.

No, if the field is changing with position, but not with time, there is no induced electric field.
 
  • #6
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.
 
  • #7
thanks,
sorry for that stupid ques about mag field changing with position...
i don't know why i asked that?
 
  • #8
dauto said:
No, if the field is changing with position, but not with time, there is no induced electric field.

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?
 
  • #9
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?
 
  • #10
Drakkith said:
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?

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.
 
  • #11
danshawen said:
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?

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.
 

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

Can a changing magnetic field affect the motion of a charged particle?

Yes, a changing magnetic field can affect the motion of a charged particle. This is because a changing magnetic field creates an induced electric field, which can exert a force on the charged particle and cause it to accelerate or change direction.

How does a changing magnetic field affect the speed of a charged particle?

A changing magnetic field can change the speed of a charged particle by inducing an electric field, which can accelerate or decelerate the particle. The direction and magnitude of the induced electric field depends on the direction and rate of change of the magnetic field.

Can a charged particle's speed change if the magnetic field is constant?

No, a charged particle's speed will not change if the magnetic field is constant. This is because a constant magnetic field does not induce an electric field, so there is no force acting on the particle to change its speed.

How does the direction of a changing magnetic field affect the motion of a charged particle?

The direction of a changing magnetic field can affect the motion of a charged particle by changing the direction of the induced electric field. This can cause the particle to change direction or even reverse its motion.

Can a changing magnetic field change the speed of a neutral particle?

No, a changing magnetic field cannot change the speed of a neutral particle. This is because neutral particles do not have an electric charge, so they are not affected by magnetic fields. Only charged particles experience a force from a magnetic field.

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