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I need to understand the concept on how to distinguish between electric fields and magnetic fields. For example, if a negatively charge particle enters the region with a velocity of 7 m/s east and two seconds later has a velocity of 11 m/s, 44 degrees South of East, then my question is what type of field in what direction is in the region and how can I tell this for sure? Let's assume that the regions have either a uniform electric or magnetic field present.

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Magnetic force acting on a charged particle can never change the kinetic energy of the particle because whenever a particle enters a UNIFORM magnetic field, the component of magnetic field along the velocity won't exert any force and the component perpendicular to the velocity can only change the direction of the particle but not it's speed.

$\vec{F}=q\vec{v}\times \vec{B}$

$|\vec{F}|=q|\vec{v}| |\vec{B}| \sin\theta$

As you can see, any component of the uniform magnetic field parallel to (or along) the velocity, cannot exert any force because $\theta =0, \sin0 = 0$.

And the component of the magnetic field perpendicular to the velocity can exert force as $\sin{90}=1$ but the work done by this force will be zero because $\cos\theta$ becomes $0$. Therefore, this force cannot alter the particle's kinetic energy.

$W=|\vec {F}||\vec{d}|\cos\theta$

On the other hand force by the electric field can do that.

$\vec{F}=q\vec{E}$

This force can change the direction as well as the magnitude of the velocity.

In your case, both the magnitude and the direction of velocity are changing. Thus, it has to be an electric field.

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  • $\begingroup$ so let's suppose that the particle is placed at rest in the region and after a couple minutes its velocity increases towards North, in this case would the field be Magnetic since it's only changing in direction ? or would you account that is also changing in velocity and therefore it would be electric again? $\endgroup$ – Dee Feb 22 '17 at 8:45
  • $\begingroup$ If the particle is initially at rest then whatever be the direction or magnitude of magnetic field it wont be exert any force or change the velocity of the particle because the velocity of the charged particle is zero (F=qvBsin𝛳 and v=o, so F=0). It has to be electric field as the particle's velocity is increasing. $\endgroup$ – Mitchell Feb 22 '17 at 8:50
  • $\begingroup$ That makes a lot of sense, thank you so much ! @Bhavya Sharma $\endgroup$ – Dee Feb 22 '17 at 9:04
  • $\begingroup$ An electric field has to be involved, but the question does not provide enough information to say anything else. How do you tell, for instance, whether it was an electric field doing the deflection, or an electric field along the initial velocity for acceleration plus a magnetic field for the deflection? $\endgroup$ – Emilio Pisanty Feb 22 '17 at 9:30
  • $\begingroup$ If the electric field is accelerating and deflecting a particle at the same time then there has to be some angle between the velocity and the electric field. So the one component accelerates the particle in one direction and the other component accelerates in other direction and results in deflection. It has to be specified whether there is electric field or magnetic field in the region (Or both). But if it is given that the electric field is along the direction of velocity and yet, the path of the particle isn't straight then it can be said that there is a magnetic field in the region. $\endgroup$ – Mitchell Feb 22 '17 at 9:40
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Magnetic force is cross product of charge×velocity and magnetic field. Hence a magnetic force is always perpendicular to velocity. A force perpendicular to velocity only changes its direction.

So the field is electric field as the velocity is increasing.

So if velocity increase it is electric field and if only direction changes it is magnetic field.

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  • $\begingroup$ so the charge doesn't matter? lets that instead of having a negative charged particle we have a positive charged particle? $\endgroup$ – Dee Feb 22 '17 at 8:42
  • $\begingroup$ Of course the charge does matter instead of negative if you take positive charge the direction of magnetic and electric force will be exactly in opposite direction than the previous one. $\endgroup$ – ATHARVA Feb 22 '17 at 8:45
  • $\begingroup$ ohhh okay i see now, one more question, so if the velocity remained the same and only its direction changed , then would that mean it has a magnetic field? or perhaps in another case in where the velocity and the direction don't change , would that be a magnetic field as well? $\endgroup$ – Dee Feb 22 '17 at 8:47
  • $\begingroup$ If velocity changes irrespective of direction changes or not changes it is electric. And when direction changes without change in velocity it is magnetic. When neither velocity not direction changes both field are absent or magnetic field is present but the object is as rest . $\endgroup$ – ATHARVA Feb 22 '17 at 8:53
  • $\begingroup$ When object is at rest in magnetic field the magnetic force is zero. $\endgroup$ – ATHARVA Feb 22 '17 at 8:57
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I need to understand the concept on how to distinguish between electric fields and magnetic fields.

Note the Wikipedia electromagnetic field article : "Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole — the electromagnetic field". An electron doesn't have an electric field or a magnetic field, it has an electromagnetic field. Also see what Minkowski said in Space and Time:

"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".

The electorn has an electromagnetic field, and electromagnetic field interactions result in linear electric force and rotational magnetic force. When we only see the former we talk of an electric field, when we only see the latter we talk of a magnetic field. There's a magnetic field around the current-in-the-wire because the linear forces cancel but the rotational forces don't.

For example, if a negatively charge particle enters the region with a velocity of 7 m/s east and two seconds later has a velocity of 11 m/s, 44 degrees South of East, then my question is what type of field in what direction is in the region and how can I tell this for sure?

There's not enough information here. Take a look at this picture of electron deflection from The Electronic Science Tutor by Georges Delpierre and Trevor Sewell:

enter image description here

You can contrive your electric and magnetic fields to deflect your electrons one way or another.

Let's assume that the regions have either a uniform electric or magnetic field present.

I don't like that assumption for various reasons. And I don't think it helps anyway. What you need is a further measurement of the particle motion to distinguish between linear and rotational force.

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