Charged particle in magentic field problem

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Homework Help Overview

The discussion revolves around a problem involving a deuteron moving in a magnetic field, specifically focusing on its circular motion, the angle between its velocity and the magnetic field, and calculations related to its speed and time for half a revolution.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the velocity vector and the magnetic field, questioning how to determine the angle without knowing the speed. There are attempts to clarify the nature of the forces acting on the particle and the implications of its circular motion.

Discussion Status

Participants are exploring the implications of the particle's motion in a magnetic field and the conditions under which the velocity vector and magnetic field interact. Some guidance has been offered regarding the perpendicular nature of the vectors involved, but there remains uncertainty about the calculations required for part (i).

Contextual Notes

There is an ongoing discussion about the assumptions related to the motion of the particle, particularly regarding the components of velocity in relation to the magnetic field. The original poster expresses confusion about the requirements of the problem, especially concerning the angle calculation.

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Homework Statement



A deuteron (the nucleus of an isotope of hydrogen) has a mass 3.34× 10−27 kg
and a charge of +1.60 × 10−19 C. The deuteron travels in a circular path with
a radius of 7.32mm in a magnetic field with magnitude 2.00T.
(i) What is the angle between the velocity and magnetic field vectors?
(ii) Calculate the speed of the deuteron.
(iii) Calculate the time required for it to make half a revolution.

Homework Equations



F=qVBsin(theta)

R=(mv)/(qB)

The Attempt at a Solution



I think I know how to solve parts ii and iii using the second equation listed, rearranged for V, then the time period would be ((pi)R)/V (half revolution)

However with part i it seems to me there is no way of calculating the angle without knowing V? Am I missing something here? It seems stupid that they would ask for a calcualtion including V without working it out first, which comes after
 
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What is the direction of the force the magnetic field exerts on the particle?

ehild
 
ehild said:
What is the direction of the force the magnetic field exerts on the particle?

ehild

Is that a question you know the answer to and are asking me to think about or is it something you want to know haha sorry I'm a bit confused. The force will be perpendicular to the field and the velocity using the right hand screw rule
 
Perfect. The force is the same as the centripetal force for the circular orbit the particle travels. This plane of the circle is perpendicular to the magnetic field. The velocity vector is in the same plane as the circle, is not it?

If the velocity of the particle were not perpendicular to the magnetic field, that is, it had both a parallel and normal component, the magnetic field would not influence the parallel component, the particle would move along a helix.

ehild
 
ehild said:
Perfect. The force is the same as the centripetal force for the circular orbit the particle travels. This plane of the circle is perpendicular to the magnetic field. The velocity vector is in the same plane as the circle, is not it?

If the velocity of the particle were not perpendicular to the magnetic field, that is, it had both a parallel and normal component, the magnetic field would not influence the parallel component, the particle would move along a helix.

ehild

Still not sure how to solve the angle for part (i) though!
 
What do you think? The particle moves in a plane that is perpendicular to the magnetic field. Can the velocity vector point out of this plane? What is the angle between any vector in-plane and the magnetic field?

ehild
 
ehild said:
What do you think? The particle moves in a plane that is perpendicular to the magnetic field. Can the velocity vector point out of this plane? What is the angle between any vector in-plane and the magnetic field?

ehild

No the magentic force is perpendicular to both the vector and magnetic field vectors. This means the field and the velocity vectors are in the same plane. Thus they are not always perpendicular.
 
The particle moves along a circle with uniform speed. The circle defines the plane in which both the velocity and the force lie. The force is radial, and rotates around while the particle is moving. The magnetic field is perpendicular to the force at every instant: it is normal to the plane of the circle. The velocity also lies in the plane of the circle. If a vector is normal to a plane, it is perpendicular to every vector lying in the plane.

ehild
 
ehild said:
The particle moves along a circle with uniform speed. The circle defines the plane in which both the velocity and the force lie. The force is radial, and rotates around while the particle is moving. The magnetic field is perpendicular to the force at every instant: it is normal to the plane of the circle. The velocity also lies in the plane of the circle. If a vector is normal to a plane, it is perpendicular to every vector lying in the plane.

ehild

sorry it seems I have become very confused. You are correct, i apologise for my questioning of your knowledge :)
 
  • #10
Well, one never knows who is there at the other end.
I suppose you know the answer to part i now?

ehild
 
  • #11
ehild said:
Well, one never knows who is there at the other end.
I suppose you know the answer to part i now?

ehild

Very true... If I'm assuming all my understanding is now correct, there is no calculation to part i, just the fact that they are perpendicular ie 90 degrees
 
  • #12
The circular orbit is crucial. If the particle had a component parallel with B, it would move along a helix. But it travels along a circle, so there is no parallel component of v.

ehild
 
Last edited:
  • #13
Drawing a picture might help a lot. I would highly recommend doing that if you haven't alreadly done it.
 

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