Question on magnetism: Circular motion of charged particle in a Magnetic Field

[physicals]

Good day,
Im a high school student currently working on my exams, I have came across a past paper question in which my answer contradicts the mark. To answer the question i used the right hand thumb rule since the direction of positive charge movement is similar to conventional current and figured out the direction of the magnetic field would be into the page A. However the real answer seems to be B (according to the mark scheme). After some thinking i reasoned that it had something to do with centripetal or centrifugal force which would require the left hand rule, but i still don't understand clearly why it is B.

 

[PeroK]

In what direction is the force on the particle?

 

[physicals]

inward towards the center (centripetal force)?

 

[A.T.]

To answer the question i used the right hand thumb rule ... centripetal or

Have you heard of the Lorentz force? Look it up, and how you use the hand to determine it's direction.

 

[PeroK]

inward towards the center (centripetal force)?

Yes. And what is the Lorentz force law in this case?

 

[physicals]

is there a basic high school level explanation because im pretty sure our syllabus didnt expect students to know Lorentz force law

 

[PeroK]

is there a basic high school level explanation because im pretty sure our syllabus didnt expect students to know Lorentz force law

The Lorentz force is the force of an electric or magnetic field on a charged particle. You may have called it so something else.

The Lorentz force law involves a right hand rule.

 

[physicals]

i thought it was flemings left hand rule. How do we relate this with the question, is there not a strait up solid answer

 

[PeroK]

i thought it was flemings left hand rule.

Apparently that's the same for a magnetic field. You have to know which finger matches which vector.

 

[PeroK]

How do we relate this with the question, is there not a strait up solid answer

The straight answer is that the magnetic field is out of the page. Answer B.

 

[physicals]

but Chatgpt said its meant to be A and its a mark scheme error with a bit of reasonable justification. Please refer to this link: https://chatgpt.com/share/6845a79a-6734-800b-9a5b-8f926625ce91 or i can send individual screen shots if you don't want to access the link

 

[PeroK]

but Chatgpt said its meant to be A and its a mark scheme error with a bit of reasonable justification. Please refer to this link: https://chatgpt.com/share/6845a79a-6734-800b-9a5b-8f926625ce91 or i can send individual screen shots if you don't want to access the link

I would do it using vectors. Assume the circle is in the x-y plane, with the positive x-axis to the right,the positive y-axis upwards and the positive z-axis out of the page.

Note that the charge is positive.

The Lorentz force is:$$\vec F = q\vec v \times \vec B$$When the velocity is in the positive x direction, the force is in the negative y direction. This implies the field is in the positive z direction, as:
$$\vec i \times \vec k = -\vec j$$

 

[PeroK]

If the charge were negative and moving clockwise, then the field would be into the page.

 

[vela]

To answer the question i used the right hand thumb rule since the direction of positive charge movement is similar to conventional current and figured out the direction of the magnetic field would be into the page A.

Can you explain in detail how you arrived at your answer? My initial impression was that you were finding the direction of the field produced by the current loop rather than answering the actual question asked.

 

[physicals]

yes i did consider the field around the loop instead of the actual direction of the magnetic field, but whats the difference?

 

[PeroK]

yes i did consider the field around the loop instead of the actual direction of the magnetic field, but whats the difference?

In this problem, there is assumed to be a uniform magnetic field. A charged particle is fired into that magnetic field and, in general, moves in a circle. Or, even more generally, in a helix.

The direction of the circular motion depends on the sign of the charge and the direction of the magnetic field. As described by the Lorentz force law.

 

[vela]

yes i did consider the field around the loop instead of the actual direction of the magnetic field, but whats the difference?

I don't understand your reply. What exactly do you mean by "field around the loop" and "actual direction of the magnetic field"?

 

[A.T.]

yes i did consider the field around the loop instead of the actual direction of the magnetic field, but whats the difference?

If they ask you whether the magnetic field goes into or out of the picture, then it can only mean the strong field applied externally.

The magnetic field generated by the moving charges, doesn't point in the same direction everywhere, so it cannot be what is asked.

 

[Steve4Physics]

To answer the question i used the right hand thumb rule since the direction of positive charge movement is similar to conventional current and figured out the direction of the magnetic field would be into the page

There are a number of different rules for different situations. It sounds like you have used the wrong rule (or used a correct rule incorrectly)!

The rule you need depends on the situation. In this problem, a force arises on the moving charges due to a magnetic field., You need to relate:
- the direction of the current;
- the direction of the magnetic field;
- the direction of the force produced.

I was taught to use 'Fleming left-hand motor rule' in this situtation:

There are equivalent alternatives which use the right hand. If you want to look them up, use a search term such as "right hand rule force current magnetic field" (and look at the images).

 

[PeroK]

I have difficulty getting my fingers in the required configuration, so I've never learned any of these rules. I use the Cartesian coordinate axes and the cyclic rule for cross products.

 

[physicals]

i sort of get all of this but there is no base level reasoning for why the mark scheme is right (if its right in the first place). We are clearly not meant to know anything above Flemings left hand rule, right hand grip rule, centripetal forces (for circular motion) and magnetic field induction.

 

[physicals]

i think this might be some what of a good reasoning though it depends on perspective. The direction of the magnetic field around the positive particle is indeed into the page but that doesn't automatically mean the direction of magnetic field causing the motion is into the page. To verify that we, know that for circular motion we need a centripetal force acting inwards towards center of orbit, thus the direction of the external magnetic field causing motion must be the same as direction of magnetic field created around the positive particle since when like directional magnetic field comes close the source of fields experience an attractive force (centripetal force in this case). so in conclusion, the answer must be A in multiple perspectives (mark scheme probably made a mistake).

 

[PeroK]

What a waste of time and effort!

 

[Steve4Physics]

i sort of get all of this but there is no base level reasoning for why the mark scheme is right (if its right in the first place).

The mark scheme is correct. Answer B.

Note that the question is not primarily intended as an exercise in reasoning. It is probably intended as an exercise in using and applying certain knowledge specified in your syllabus.

We are clearly not meant to know anything above Flemings left hand rule, right hand grip rule, centripetal forces (for circular motion) and magnetic field induction.

Why do you say that? I'd say the opposite is true.

but Chatgpt said its meant to be A and its a mark scheme error with a bit of reasonable justification.

ChatGPT is wrong! Surprise! Shock! Horror!

The direction of the magnetic field around the positive particle is indeed into the page

No. The moving positive particle produces a circular field: outside the orbit, the field is out of the page; inside the orbit, the field is into page.

but that doesn't automatically mean the direction of magnetic field causing the motion is into the page. To verify that we, know that for circular motion we need a centripetal force acting inwards towards center of orbit, thus the direction of the external magnetic field causing motion must be the same as direction of magnetic field created around the positive particle

No. To produce a radially inwards force, the field lines outside the particle's orbit must be more densely packed than the field lines inside the particle's orbit. This occurs when the external field is as given in answer B.

since when like directional magnetic field comes close the source of fields experience an attractive force (centripetal force in this case). so in conclusion, the answer must be A in multiple perspectives (mark scheme probably made a mistake).

No. Look at the following (current going into page) and decide if, inthe right-hand diagram, the conductor is pushed up or down.

(Diagram from https://www.schoolphysics.co.uk/age...e_on_a_current_in_a_magnetic_field/index.html)

 

[physicals]

Hey thanks for your opposition but upon checking examiner reports I have verified that the answer is truly A. It really is hard to try prove something that is the opposite of correct!

 

[PeroK]

Nevertheless, the answer to the question as stated is B.

Does anyone disagree?

 

[physicals]

I love how we members on physics forum love to debate about completely useless things even though its wrong

 

[Steve4Physics]

Hey thanks for your opposition but upon checking examiner reports I have verified that the answer is truly A. It really is hard to try prove something that is the opposite of correct!

In Post #1 you said the mark scheme says that the answer is B.

Please give a link to the examiner's report. Or give the examination board and examination date.

Edit.

 

[physicals]

here's the deal, if you can prove the answer is B using high school physics then I will send the examiners report

 

[physicals]

Thank you for everyone's time and support, i wish to close this thread, since this question is no longer needed of my interest anymore

 

[PeroK]

here's the deal, if you can prove the answer is B using high school physics then I will send the examiners report

The answer is B whether you use the Lorentz force law or the Fleming rule.

 

[physicals]

With learning must come humility and acceptance as well, i am sorry to have lied about the examiner report, after some proper thinking i have concluded that the right answer is B, using my earlier reasoning for the centripetal force and magnetic force, the magnetic field indeed goes into the page. But were all this confusion really came from is this (Flemings right hand rule here is Lorentz force law) i dont understand the difference between the two:

 

[vela]

For the left-hand rule, the current is the input and force is the output. That is, it tells you how to calculate the direction of $\vec F = I \vec l \times \vec B$ given a current moving in the direction of $\vec l$ in a field $\vec B$. For the right-hand rule, the roles are switched. The motion (misleadingly called force in the diagram) is the input, and the current is the output. It tells you how the calculate the direction of $\vec F = q \vec v \times \vec B$, the force exerted on a charge moving with velocity $\vec v$ in a magnetic field $\vec B$. The force on the charge may cause the charge to move, producing a current.

Both rules are actually the Lorentz force law, but you have to identify the quantities in the problem correctly.

 

[physicals]

so the magnetic field pushes the particle instead of pull? then how is there circular motion?

 

[PeroK]

so the magnetic field pushes the particle instead of pull? then how is there circular motion?

A force is a force. A force of constant magnitude that is always perpendicular to the velocity results in circular motion.