# Magnetic Field Lines & Force

• I
Hello,

I am unable to understand a certain (important) concept.

We all know what the field lines of a permanent magnet look like. They go from north to south, and curve around the magnet.

This direction (direction of the magnetic field) does NOT describe the direction of a force. And that's where I am confused.

Say I cut another stick magnet in half, and only use the magnetic north pole portion. If I were to put this below the south pole of my original magnet, it would start moving towards it (you could start a discussion on relativity here, but that's not what I am trying to do).Likewise, if I were to put it on the north pole it would move away from the magnet.

Wouldn't that mean that the force is in the same direction as the field lines?

EDIT: someone said you can't cut a magnet in half. I know. It was ment to be a thought experiment.

-Yael

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ZapperZ
Staff Emeritus
Hello,

I am unable to understand a certain (important) concept.

We all know what the field lines of a permanent magnet look like. They go from north to south, and curve around the magnet.

This direction (direction of the magnetic field) does NOT describe the direction of a force. And that's where I am confused.
This is true for moving charged particles. It is not true for another magnet, as you described in the rest of your post.

Zz.

This is true for moving charged particles. It is not true for another magnet, as you described in the rest of your post.

Zz.
So for another magnet the force on said magnet IS the same as the magnetic field (direction wise),
and for a charged particle the force isn't in the same direction (use right hand rule)?

-Yael

sophiecentaur
Gold Member
2020 Award
does NOT describe the direction of a force.
You are making the wrong conclusion here. A field is described in terms of a force. In the case of a magnetic field, it is still defined as the direction that an isolated magnetic North Pole would be pushed. We do not have isolated magnetic poles but the definition is 'ok'; a small compass needle is pulled by each pole of the magnet and will lie on a field line but is cannot move because each end is being pulled.
But there is a 'fudge' which can actually demonstrate the force on a (nearly) isolated Pole.
I used to give a demonstration of this to lower school kids and it was very impressive. I cannot find a mention of it on Google but I can describe it.
You take a long magnetised knitting needle and stick it into a cork, with the cork very near one end. You float it (upright) in a large deep bowl of water. You then hold a (not too strong) bar magnet, horizontally just above the water. The needle, incredibly, will move slowly through the water and follow the classic line of force pattern from one pole to the other. It works because the 'other' pole of the needle is well away from the bar magnet. The needle tilts a bit, of course and if the magnet is too strong, it will tip over and be pulled to lay horizontally along the magnet.
Someone really needs to set that up in a school lab and video it for YouTube.
[Edit: I managed to find one video of the demo, which is not as good as the one we used to do at my school]

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magnetics
ZapperZ
Staff Emeritus
So for another magnet the force on said magnet IS the same as the magnetic field (direction wise),
and for a charged particle the force isn't in the same direction (use right hand rule)?
Yes. You may verify the former with a compass.

Zz.

sophiecentaur
Gold Member
2020 Award
This is true for moving charged particles. It is not true for another magnet, as you described in the rest of your post.

Zz.
It's not quite as simple as that and needs a bit more description, I think. The particles are basically deflected to one side of the field lines but their path can be spiral around the lines. If they arrive in the field at a suitable angle, they can be 'captured' by the field lines and follow them. It is a phenomenon that can be seen as high speed charged particles spiral around the Earth's field lines and cause the Aurora at the Poles.

ZapperZ
Staff Emeritus
It's not quite as simple as that and needs a bit more description, I think. The particles are basically deflected to one side of the field lines but their path can be spiral around the lines. If they arrive in the field at a suitable angle, they can be 'captured' by the field lines and follow them. It is a phenomenon that can be seen as high speed charged particles spiral around the Earth's field lines and cause the Aurora at the Poles.
The component of the motion along the field lines is not due to a "force". It is due to the initial motion. If the charge particles enter the field without any velocity component along the direction of the field, it will simply move in a circle, not a spiral.

Zz.

sophiecentaur
Gold Member
2020 Award
The component of the motion along the field lines is not due to a "force". It is due to the initial motion. If the charge particles enter the field without any velocity component along the direction of the field, it will simply move in a circle, not a spiral.

Zz.
The Force is not in the direction of the lines in that case. The Force is the Vector Product of velocity and field, which is at right angles to the field line.

ZapperZ
Staff Emeritus
The Force is not in the direction of the lines in that case. The Force is the Vector Product of velocity and field, which is at right angles to the field line.
But isn't that what I implied when I told the OP that his/her original premise that the force is NOT along the magnetic field lines is true for charge particles?

I hope you are not thinking that I'm ignorant of the Lorentz force equation.

Zz.

The Force is not in the direction of the lines in that case. The Force is the Vector Product of velocity and field, which is at right angles to the field line.
If the initial velocity (of a charged particle) is zero there is no force on the particle. That's what I was taught atleast. Is that not true
But isn't that what I implied when I told the OP that his/her original premise that the force is NOT along the magnetic field lines is true for charge particles?

I hope you are not thinking that I'm ignorant of the Lorentz force equation.

Zz.
If the initial velocity is zero, what is the direction of the force? I am not as ignorant as I may come across, but there's definitely some confusion on my part.
Wouldn't the force be zero?

ZapperZ
Staff Emeritus
If the initial velocity is zero, what is the direction of the force? I am not as ignorant as I may come across, but there's definitely some confusion on my part.
Woulnd't the force be zero?
I'm getting all confused here. You are replying to my post that was directed at another member.

The Lorentz force equation that involves JUST the magnetic field part is

F = qv × B

This is assuming that you know what a "cross product" means. You'll notice that from this equation, the magnetic force on the charge particle q depends on (i) the velocity v of the charge particle, (ii) the charge on the charge particle, (iii) the strength of the magnetic field B, and (iv) the ANGLE between v and B.

The force is maximum if v is perpendicular to B. The force is ZERO if v=0, i.e. the charge particle isn't moving.

Zz.

I'm getting all confused here. You are replying to my post that was directed at another member.

The Lorentz force equation that involves JUST the magnetic field part is

F = qv × B

This is assuming that you know what a "cross product" means. You'll notice that from this equation, the magnetic force on the charge particle q depends on (i) the velocity v of the charge particle, (ii) the charge on the charge particle, (iii) the strength of the magnetic field B, and (iv) the ANGLE between v and B.

The force is maximum if v is perpendicular to B. The force is ZERO if v=0, i.e. the charge particle isn't moving.

Zz.
I know it was directed at another member, but your messages made me think up a new question.

I also know what a "cross product" is. Just because my English is pretty basic doesn't mean I don't understand basic math.
That's the beautiful part of science. It's language (math) is universal, although the language used in order to discuss these things isn't.

Thanks for the answers. They were crystal clear.

-Yael

sophiecentaur
Gold Member
2020 Award
But isn't that what I implied when I told the OP that his/her original premise that the force is NOT along the magnetic field lines is true for charge particles?

I hope you are not thinking that I'm ignorant of the Lorentz force equation.

Zz.
It can be difficult to get such a sophisticated message across in a very few words. I would say that the path of a spiralling particle along a field line is a pretty good demonstration of a force acting - but of course the force is not along the field line.
I didn't say you were wrong. I said it needed to be made a bit more clear. Of course we know the Lorenz force and it doesn't act along the field lines; motion of the charge is necessary (again, as we know). It may perhaps have been better not to have brought it up in this context. The definition is based on a (conceptual) Pole and not a current.

ZapperZ
Staff Emeritus
I also know what a "cross product" is. Just because my English is pretty basic doesn't mean I don't understand basic math.
That's the beautiful part of science. It's language (math) is universal, although the language used in order to discuss these things isn't.
I wasn't referring to your comprehension of English. Since you did not describe what level you are at, I have no idea if you are already aware of the relevant mathematics.

Zz.

sophiecentaur