Coulomb's force vs the Lorentz force

[Electrodude]

Beams of electrons and protons move parallel to each other in the same direction. They ______.
a. attract each other.
b. repel each other.
c. neither attract nor repel.
d. the force of attraction or repulsion depends upon the speed of the beams.

This is a previous-year-question of CBSE Board 2023.
The answer key marks (b) as the right option.
I want to know why we are ignoring Coulomb's force?

 

[PeroK]

Beams of electrons and protons move parallel to each other in the same direction. They ______.
a. attract each other.
b. repel each other.
c. neither attract nor repel.
d. the force of attraction or repulsion depends upon the speed of the beams.

This is a previous-year-question of CBSE Board 2023.
The answer key marks (b) as the right option.
I want to know why we are ignoring Coulomb's force?

What happens if the speed of both beams is zero, or approximately zero?

 

[Dale]

This is a poorly worded question. Are they talking about one pair of beams one containing protons and the other electrons? Or one pair of beams each containing both protons and electrons? Or multiple pairs of beams one pair entirely of protons and another pair entirely of electrons?

 

[Electrodude]

This is a poorly worded question. Are they talking about one pair of beams one containing protons and the other electrons? Or one pair of beams each containing both protons and electrons? Or multiple pairs of beams one pair entirely of protons and another pair entirely of electrons?

This is the exact question. This question probably was prompted to around a million students two years back.
Anyways, with reference to the complexity level of our syllabus, it would be safe to assume that there are two separate beams of electrons and protons, some unspecified distance apart and travelling at some unspecified speed.

 

[Electrodude]

What happens if the speed of both beams is zero, or approximately zero?

Is it to assume static conditions to apply electrostatics?

 

[PeroK]

This is the exact question. This question probably was prompted to around a million students two years back.
Anyways, with reference to the complexity level of our syllabus, it would be safe to assume that there are two separate beams of electrons and protons, some unspecified distance apart and travelling at some unspecified speed.

Speed is frame dependent. Take the case where the speeds are equal and consider the frame where that speed is zero. Now we have two rows of protons and electrons at rest that repel each other?

 

[haruspex]

I'd forgotten this puzzled me in the past: whether there is a magnetic field from a current must depend on the frame of reference. Turns out it takes SR to explain it.
Consider two parallel beams of electrons at the same velocity. The relative motion to the observer increases the electrostatic repulsion, and this exactly cancels the attraction created by the observed magnetic fields.
Full details at https://physics.stackexchange.com/q...forces-on-each-other-depending-on-frame-of-re.

So the answer to the question in this thread is a.

 

[PeroK]

This question can be understood without relativity by considering a reference frame in which the beams move at the same speed in opposite directions. That's equivalent to two equal currents in the same direction, which produces an attractive force. Additionally, if we have beams of particles rather than neutral current carrying wires, then there is an additional attractive electric force.

 

[haruspex]

This question can be understood without relativity by considering a reference frame in which the beams move at the same speed in opposite directions.

I do not understand. If they move with the same velocity in one frame they must move at the same velocity in all frames.
Besides, the conundrum is why two different inertial frames appear to give conflicting results. Considering a third frame cannot resolve that.

Btw, it remains true, of course, that two parallel wires carrying (vectorially) the same current attract, but a wire carrying a current is not the same as a beam of ions: it has no net charge. That said, I have not figured out why an observer moving with the same velocity as the electrons still sees attraction. Maybe it looks like positive charges moving the other way?

 

[kuruman]

To muddy the waters some more, here is one of the many sites that feature this question
https://www.shaalaa.com/question-ba...ther-in-the-same-direction-they-_______356772
In it, the "correct" answer is as reported by the OP,

and farther down is the explanation of sorts

So I looked at the AI overview and I found concurrence that there be repulsion

Just to make sure, I "dove deeper" into AI and guess what?

Yay, there is attraction now !!!

I don't think that the physical situation of charged beams moving in vacuum can be be made equivalent to electrons confined to move within an overall neutral conductor.

 

[PeroK]

I do not understand. If they move with the same velocity in one frame they must move at the same velocity in all frames.

If they move with the same velocity in the "lab" frame, then the frame in which they move with the same velocity in opposite directions is, degenerately, the rest frame. And, in that frame, there is simply electrostatic attraction.

It did not specify in the question that the speeds of the beams were the same. I was considering the more general case.

Besides, the conundrum is why two different inertial frames appear to give conflicting results. Considering a third frame cannot resolve that.
Btw, it remains true, of course, that two parallel wires carrying (vectorially) the same current attract, but a wire carrying a current is not the same as a beam of ions: it has no net charge. That said, I have not figured out why an observer moving with the same velocity as the electrons still sees attraction. Maybe it looks like positive charges moving the other way?

As these are beams of particles, not neutral current-carrying wires, we can't ignore the electric force. In the case where the velocities are the same, we have attraction in the rest frame. In a frame where the beams are moving, we have a magnetic repulsion. But, considering length contraction in this frame makes the beams more intense and increases the electric attraction.

In any case, the electric force must dominate in all frames.

 

[haruspex]

If they move with the same velocity in the "lab" frame, then the frame in which they move with the same velocity in opposite directions is, degenerately, the rest frame. And, in that frame, there is simply electrostatic attraction.

I must be misinterpreting what you are saying. As I read the above, you are saying that if in one frame they are both moving at velocity $\vec v$ then there is some other frame, moving at $\vec u$ wrt the first frame, say, in which the velocities (both $\vec v-\vec u$) are now equal and opposite. Seems to me that implies $\vec v=\vec u$.

It did not specify in the question that the speeds of the beams were the same. I was considering the more general case.

No, you specified "same velocity".
I think what you are intending to say is that if they are moving at parallel but different velocities then there is a frame in which they are moving with equal and opposite velocities. Well, of course, but that only gives a way of solving the general problem by choice of a particular frame (as you already did for the equal velocity case in post #6) ; it doesn’t give a way of understanding the difficulty that whether there is a magnetic (Lorentz) force in the equal velocity case seems to depend on the choice of frame. That requires SR.

Our disagreement seems to hinge on what is meant by "understanding the problem".

As these are beams of particles, not neutral current-carrying wires,

As I also noted in post #9.

In a frame where the beams are moving, we have a magnetic repulsion. But, considering length contraction in this frame makes the beams more intense and increases the electric attraction.

Exactly.

 

[PeroK]

As I read the above, you are saying that if in one frame they are both moving at velocity $\vec v$ then there is some other frame, moving at $\vec u$ wrt the first frame, say, in which the velocities (both $\vec v-\vec u$) are now equal and opposite. Seems to me that implies $\vec v=\vec u$.

Trivially, if the speeds are $u > v$, then (in the non-relativistic approximation), there is a frame where the speeds are $\frac{u - v} 2$ in opposite directions.

No, you specified "same velocity".

I took equal speeds as a special case to illustrate the point.

I think what you are intending to say is that if they are moving at parallel but different velocities then there is a frame in which they are moving with equal and opposite velocities.

Zero is still a valid velocity in my book. In general, they are different, with the same speed being a special case.

 

[PeroK]

This is the exact question. This question probably was prompted to around a million students two years back.
Anyways, with reference to the complexity level of our syllabus, it would be safe to assume that there are two separate beams of electrons and protons, some unspecified distance apart and travelling at some unspecified speed.

From what I've seen, there are a lot of bad questions out there now. And a lot of wrong explanations. The common theme seems to be people who do not understanding physics changing a scenario and not understanding the impact of the changes. In this case, for example, neutral current-carrying wires have been replaced by beams of charged particles. And, whoever did that, as you yourself pointed out, completely forgot about Coulomb's law!

My advice is to keep your wits about you and trust yourself to some extent. A reliable textbook is unlikely to be wrong. But, these multiple choice question papers are littered with poorly phrased questions, wrong answers and wrong explanations.

Note also that @kuruman induced AI to give both the wrong answer and the right answer. There is a good lesson there as well about the limitations of LLM's. Again, keep your wits about you and double-check what you find online.

 

[Electrodude]

To muddy the waters some more, here is one of the many sites that feature this question
https://www.shaalaa.com/question-ba...ther-in-the-same-direction-they-_______356772
In it, the "correct" answer is as reported by the OP,
View attachment 367007
and farther down is the explanation of sorts

View attachment 367008
So I looked at the AI overview and I found concurrence that there be repulsion

View attachment 367009
Just to make sure, I "dove deeper" into AI and guess what?

View attachment 367010
Yay, there is attraction now !!!

I don't think that the physical situation of charged beams moving in vacuum can be be made equivalent to electrons confined to move within an overall neutral conductor.

According to the marking scheme for this question paper (This is from 12th Physics CBSE Board 2023) the correct answer is option (b).

 

[Dale]

According to the marking scheme for this question paper (This is from 12th Physics CBSE Board 2023) the correct answer is option (b).

That answer would only be correct if the question meant that both beams in the pair were composed of protons or both beams were composed of electrons.

 

[PeroK]

According to the marking scheme for this question paper (This is from 12th Physics CBSE Board 2023) the correct answer is option (b).

You must forgive the heresy here at Physics Forums, where we call into question the infallability of the 12th Physics CBSE Board!

 

[kuruman]

According to the marking scheme for this question paper (This is from 12th Physics CBSE Board 2023) the correct answer is option (b).

Please provide links or references. As I pointed out in post #10, there is at least one site that shows repulsion (option b) as the correct answer. However, I found this site, which appears official because it shows the pdf files with answers of the actual test, not reproductions or reinterpretations
https://www.oswaal360.com/pluginfile.php/10939/mod_folder/content/0/Latest Board Papers Files/CBSE Class 12/CBSE-12 physics Board Paper-2023.pdf
wherein the question in question is,

with the offered answer farther down

Moral: If it appears on the web, it's not automatically correct especially at points where artificial intelligence intersects natural stupidity.

 

[Electrodude]

Please provide links or references. As I pointed out in post #10, there is at least one site that shows repulsion (option b) as the correct answer. However, I found this site, which appears official because it shows the pdf files with answers of the actual test, not reproductions or reinterpretations
https://www.oswaal360.com/pluginfile.php/10939/mod_folder/content/0/Latest Board Papers Files/CBSE Class 12/CBSE-12 physics Board Paper-2023.pdf
wherein the question in question is,

View attachment 367016
with the offered answer farther down

View attachment 367017
Moral: If it appears on the web, it's not automatically correct especially at points where artificial intelligence intersects natural stupidity.

You can find the question paper here and the marking scheme here. The concerned paper is 55/2/1.
I have included snippets for convenience.

The CBSE board has its ways of bending physics to its liking. /s

 

[Dale]

Again, the question is very poor because it can be interpreted multiple ways. The only way that it can be interpreted so that the given answer is correct is if it means that both beams are protons or both beams are electrons.

 

[kuruman]

You can find the question paper here and the marking scheme here. The concerned paper is 55/2/1.
I have included snippets for convenience.
View attachment 367018
View attachment 367019
The CBSE board has its ways of bending physics to its liking. /s

Thank you for providing the references.

Again, the question is very poor because it can be interpreted multiple ways. The only way that it can be interpreted so that the given answer is correct is if it means that both beams are protons or both beams are electrons.

And since the question mentions electrons and protons, both beams being of the same kind cannot be the case. So the answer is inconsistent with the question.

 

[haruspex]

You can find the question paper here and the marking scheme here. The concerned paper is 55/2/1.
I have included snippets for convenience.
View attachment 367018
View attachment 367019
The CBSE board has its ways of bending physics to its liking. /s

It's intriguing that two authoritative-looking sources provide different answers. Maybe somebody at oswaal360 realised the CBSE answer was wrong and corrected it without comment. Or arrived at their own answer and didn’t check the original.
Unfortunately, neither source shows any sign of appreciating the subtlety that, in the lab frame, there are opposing forces, nor that this can be resolved by choice of frame. The lack of explanation makes them rather useless as teaching aids.

 

[willyengland]

Let's say I have two beams, one with protons and one with electrons, traveling parallel to each other at the same speed. I'm looking at them from above. Do the beams converge or diverge?
As a layman I would say, they converge.

 

[PeroK]

Let's say I have two beams, one with protons and one with electrons, traveling parallel to each other at the same speed. I'm looking at them from above. Do the beams converge or diverge?
As a layman I would say, they converge.

I agree, it would be odd if they diverged. To see this, consider the frame of reference moving with the beams. That is to say, the rest frame of the particles. In that frame, there is only the Coulomb attractive force.

 

[kuruman]

I agree, it would be odd if they diverged. To see this, consider the frame of reference moving with the beams. That is to say, the rest frame of the particles. In that frame, there is only the Coulomb attractive force.

Along these lines (and just for fun) I tried to imagine what will happen qualitatively in the very end. The two parallel beams sounded too complicated, so I considered four charged particles of equal mass held at the corners of a square. What will happen if they are released simultaneously? Classically, the conservation laws of mechanical energy (ignoring radiation by the accelerating particles), linear momentum and angular momentum hold.

The initial linear momentum of the CM is zero and remains zero. This means that the CM is at the center of the square at all times.

Each charge experiences a net force that produces a torque about the CM. Diagonally opposite charges experience force couples. The net effect is that the dipoles formed by diagonally opposite charges will rotate about the center of mass in opposite directions. This conserves angular momentum but not angular speed about the CM.

Finally, the initial mechanical energy of the system is in the form of the total electrostatic potential energy, $$U=-\frac{\sqrt{2}q^2}{4\pi\epsilon_0a}.$$ When the particles are released, they will spiral in towards the CM as the potential energy decreases (becomes more negative.) Mechanical energy conservation requires that the two dipoles increase their equal and opposite angular speeds about the CM.

So in the end I think this will have two counter-rotating dipoles at the center. Also interesting is a quantum mechanical description of the four-charge end result. I can imagine positronium-like atoms in the para or ortho spin state with high orbital quantum numbers.

What happens to two parallel linear distributions of many particles each is another story.

 

[Herman Trivilino]

Let's say I have two beams, one with protons and one with electrons, traveling parallel to each other at the same speed. I'm looking at them from above. Do the beams converge or diverge?
As a layman I would say, they converge.

Yes. But if you have two straight parallel wires carrying current in opposite directions, they will repel. This is probably what the question's authors were getting at. Pedagogically it requires the student to understand that a beam of electrons moving one way is equivalent to a current flowing in the opposite direction plus that the magnetic force between these wires is repulsive. A purely pedagogical consideration: Two concepts in one question makes it impossible to determine which of the two concepts is misunderstood by a student who gets it wrong.

But as others have already pointed out, a beam of charge-carrying particles is not equivalent to a current-carrying wire, so that constitutes a conceptual error by the authors at the expense (or perhaps lucky benefit) of the student. Either way, it's typical of the crappy questions we see on lots of testing and assessment instruments. It's like they were authored by a committee. And you know the old joke that a donkey is a horse built by a committee.

 

[kuruman]

And you know the old joke that a donkey is a horse built by a committee.

I thought that was a camel not a donkey.

 

[haruspex]

It's like they were authored by a committee.

I feel it’s more likely a lack of peer review. A committee might have done better.

 

[Herman Trivilino]

I feel it’s more likely a lack of peer review. A committee might have done better.

Could be both!

 

[PeroK]

The error was caused by an excess of positivity on the one hand and an excess of negativity on the other; and, a general lack of neutrality.