Direction of magnetic force

[mondo]

I am reading chapter 8th of Griffiths' electrodynamics (4th edition) on page 361 I stumbled upon this:

For figure 8.3 I don't understand why does the magnetic force of charge q1 points upward? According to right hand rule the thumb should point in the direction of v1 and then fingers curling around, show the direction of B1. This part I think is reflected on the figure because B1 points in the direction of negatve z axis. But then Fm should point in the direction of the palm which is into negative y axis while on the figure it is positive y axis, why?

PS: for Fm coming from q2 all is aligned with my right-hand rule description.

Thanks

 

[Orodruin]

Both magnetic forces look ok according to the right-hand rule. Are you comparing the correct fields for each case? Only the vectors drawn at $q_1$ (including $\vec B_2$!) are relevant to the force on $q_1$.

 

[mondo]

@Orodruin , I am talking about the Fm that is pointing upwards from charge g1 - how can it be upwards? The charge is moving to the left hence the palm rule says the magnetic force is pointing downwards.

 

[Orodruin]

@Orodruin , I am talking about the Fm that is pointing upwards from charge g1 - how can it be upwards? The charge is moving to the left hence the palm rule says the magnetic force is pointing downwards.

View attachment 358646

No. Thumb in the $\vec v_1$ direction and fingers pointing out of the page in the $\vec B_2$ direction means palm is pushing up. Unless you are using your left hand …

 

[mondo]

How is that possible? The charge moves to the left so below picture describes the situation:

So the thumb point in the direction of the charge q1, the magnetic field is into the page, but the magnetic force points down. The same rule applies to charge q2, and there it is ok, I only don't get the Fm coming out of charge q1.

@Orodruin so with the help of above picture do you still think the palm points up?

 

[Orodruin]

How is that possible? The charge moves to the left so below picture describes the situation:
View attachment 358674

So the thumb point in the direction of the charge q1, the magnetic field is into the page, but the magnetic force points down. The same rule applies to charge q2, and there it is ok, I only don't get the Fm coming out of charge q1.

@Orodruin so with the help of above picture do you still think the palm points up?

That’s a completely different right-hand rule dealing with the direction of the magnetic field generated by a current. You can use it to figure out which way the magnetic fields should be pointing - not the force on the charges (they are also correct in the picture).

At this point there is unfortunately not anything more to say other than that you are misapplying the right-hand rule.

Take the picture from post #1, put your right thumb in the direction of $\vec v_1$ (ie, pointing left) and then - without changing the direction of the thumb - put your other fingers in the direction of the magnetic field $\vec B_2$, ie, towards you. If this is uncomfortable anatomically (as is highly likely), borrow someone else’s right hand.

Barring any anatomical anomalies, your palm - and therefore the force - is now facing up.

 

[mondo]

put your other fingers in the direction of the magnetic field B→2,

But why in the direction of B2 if I want to establish magnetic field and magnetic force of q1?
Also, the magnetic field is curling around the wire, so if I curl my palm and fingers respectively and follow the magnetic field trajectory then yes at some point (assuming I can do it anatomically) my palm will point upwards. So how should I understand it?

 

[Orodruin]

But why in the direction of B2 if I want to establish magnetic field and magnetic force of q1?
Also, the magnetic field is curling around the wire, so if I curl my palm and fingers respectively and follow the magnetic field trajectory then yes at some point (assuming I can do it anatomically) my palm will point upwards. So how should I understand it?

No, again - you are trying to apply a right-hand rule that is not intended to be used to find the force. It is intended to help you find the direction of the field generated by a current.

The right-hand rule that deals with finding the force from the field and current has nothing to do with curling your fingers so forget that one if you are finding the direction of the force.

You need to take the field $\vec B_2$ at $q_1$ because that is the field that is not generated by $q_2$ and not by $q_1$ itself and therefore the field acting on $q_1$.

 

[Ibix]

We always called the diagram in #5 the "right hand grab rule" to distinguish it from the "right hand rule" in #3.

Frankly, I found it easier to remember that the Lorentz force was $q\vec v\times\vec B$ and that $\vec x\times\vec y$ points in the $+z$ direction than worry about which hand was which. Especially when my success rate on stating which side is left and which side is right is dodgy at the best of times...

 

[Orodruin]

We always called the diagram in #5 the "right hand grab rule" to distinguish it from the "right hand rule" in #3.

Frankly, I found it easier to remember that the Lorentz force was $q\vec v\times\vec B$ and that $\vec x\times\vec y$ points in the $+z$ direction than worry about which hand was which. Especially when my success rate on stating which side is left and which side is right is dodgy at the best of times...

My high-school teacher taught us the FBI right-hand pistol rule.

 

[Ibix]

My high-school teacher taught us the FBI right-hand pistol rule.

Yeah, I was taught it with a three-digit gesture like this one from the Wiki article on the right hand rule:

As a violin player and avid Mr Spock fan I had no trouble folding two fingers and pointing the rest in three different directions, but some people did. The gesture in post #3 is actually quite a lot easier to do.

 

[jtbell]

You need to take the field $\vec B_2$ at $q_1$ because that is the field that is not generated by $q_2$ and not by $q_1$ itself and therefore the field acting on $q_1$.

I think you have an extra “not”, which I’ve struck out.

To the OP, the force exerted on a point charge is not influenced by the field produced by the charge itself. This applies to both electric and magnetic fields.

 

[Orodruin]

I think you have an extra “not”, which I’ve struck out.

Indeed.

 

[Orodruin]

Yeah, I was taught it with a three-digit gesture like this one from the Wiki article on the right hand rule:
View attachment 358678
As a violin player and avid Mr Spock fan I had no trouble folding two fingers and pointing the rest in three different directions, but some people did. The gesture in post #3 is actually quite a lot easier to do.

Turning to page 4 of my book, we see that I can also do it

(it is actually a photo of my hand somewhat processed by GIMP with added vectors on top)

 

[mondo]

I think you have an extra “not”, which I’ve struck out.

To the OP, the force exerted on a point charge is not influenced by the field produced by the charge itself. This applies to both electric and magnetic fields.

Yes the 'not' seems to be wrong there, but this post helped me to catch my main problem - I initially thought that Fm at point q1 is there due to the magnetic force generated by q1 itself. While this is a force in response to the magnetic field of charge q2 alone.

Thank you all again for the help! :)

 

[Orodruin]

I initially thought that Fm at point q1 is there due to the magnetic force generated by q1 itself.

Note that the field of q1 at q1 itself is not well defined and therefore also does not have a well defined direction. Just like its electric field at its own position has no well defined direction.

 

[mondo]

Note that the field of q1 at q1 itself is not well defined and therefore also does not have a well defined direction. Just like its electric field at its own position has no well defined direction.

It is a good point. The electric field I think is well defined - it needs to point away from both charges at they both repeal each other, right?
As for the magnetic field, it is supposed to curl around the x axis as the charge is moving. Both direction are also mentioned by the author on the previous page.

 

[jtbell]

Nevertheless, at the location of the (point) charge, the direction of the field that it produces is not well-defined. For the electric field, at the location of the charge, there is no unique direction that points "away from the charge." All directions point away from the charge!

For that matter, the magnitude of the field at the location of the charge is also undefined, because it would be $$E = \frac {kq} 0$$

 

[mondo]

@jtbell , I understand the problem is that the charge is moving, but we can describe its position quite accurately as it moves along x axis - it's just f(x) = 0; So I think if we express both charges position in some way then we can always calculate the distance between them and hence the electric field, right?

Why do you have 0 in the denominator of your E formula? It is supposed to be a distance to the other charge right?

 

[Ibix]

So I think if we express both charges position in some way then we can always calculate the distance between them and hence the electric field, right?

The problem is the field of the charge itself. You can calculate the field of charge 1 at the location of charge 2 and vice versa easily enough. It's the field of charge 1 at the position of charge 1 that's the problem. With a classical point charge, it's undefined - the field strength goes to infinity as the distance goes to zero (that's where the zero in the denominator of @jtbell's expression comes from) and there's no unique direction that's away from itself.

 

[Orodruin]

@jtbell , I understand the problem is that the charge is moving, but we can describe its position quite accurately as it moves along x axis - it's just f(x) = 0; So I think if we express both charges position in some way then we can always calculate the distance between them and hence the electric field, right?

That the charge is moving is not a problem at all. The problem is that you cannot define a direction of the field of a point charge at the position where that charge is located.

Why do you have 0 in the denominator of your E formula? It is supposed to be a distance to the other charge right?

It is the distance to the charge generating the field. If you look at the field at the position of the generating charge, that field does not have a well defined direction. Which is what we were saying.

The field at the position of thd other charge is well defined.

 

[mondo]

Okay but this is true for any charge in any configuration - a location of its own electric field is undefined, right? However a direction and magnitude of an electric field from this charge to any other (test) charge is well defined and given by Coulomb's law.

 

[Orodruin]

Okay but this is true for any charge in any configuration - a location of its own electric field is undefined, right? However a direction and magnitude of an electric field from this charge to any other (test) charge is well defined and given by Coulomb's law.

Yes, but we have to remember how we got here: you tried to apply the right-hand rule using the particle’s own field.

 

[mondo]

Yes, but we have to remember how we got here: you tried to apply the right-hand rule using the particle’s own field.

heh right, thank you (and everyone involved) for a lesson .

 

[A.T.]

The gesture in post #3 is actually quite a lot easier to do.

Sure, but it distinctly inticates just 2 directions . How do you memorize that the force comes out of the palm and not the back of the hand? You can't tell students "It's the way you bi*ch slap somebody".

PS: You can't even write it on this forum. It gets changed to "jerk", which confusingly is a different physical quantity.

 

[Ibix]

How do you memorize that the force comes out of the palm and not the back of the hand?

It doesn't seem much harder than remembering whih quantity is associated with which finger.

Actually, isn't vector area a cross-product? Associating the vector area of your palm with the force should work even under reflection!

 

[A.T.]

It doesn't seem much harder than remembering whih quantity is associated with which finger.

Using the gesture below, it's quitle logical: The order of the fingers is the same as in writing down the cross product:

e1 x e2 = e3

In fact, I always start with a closed fist, and extend them one by one in that order.

 

[Orodruin]

How do you memorize that the force comes out of the palm and not the back of the hand? You can't tell students "It's the way you bi*ch slap somebody".

... but you can tell them that is the direction you usually use your hand to push something.