Direction of a particle in a uniform magnetic field.

In summary, the question is asking to show that when the x component of the displacement of a particle with velocity v^vector is 2 * Pi * (m / qB) * vcos(theta), the velocity of the particle remains in the same direction as it was when it entered a region with a uniform magnetic field B^vector in the +x direction. This can be proven by considering the displacement in the x-direction, (vcosθ)t, and using the equation for the period of circular motion, T = 2 * Pi * m / q * B.
  • #1
nvictor
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0

Homework Statement



a beam of particles with velocity v^vector enters a region that has a uniform magnetic field B^vector in the +x direction.

show that when the x component of the displacement of one of the particles is 2 * Pi * (m / qB) * vcos(theta), where theta is the angle between v^vector and B^vector, the velocity of the particle is in the same direction as it was when the particle entered the field

Homework Equations



the period of circular motion is T = 2 * Pi * m / q * B

The Attempt at a Solution



if I divide v = d * t = x * t

if I choose t to be T then I find v = v cos(theta).

then thing is, I don't really undertstand the question, and I want to know how to proceed from there.
 
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  • #2
Hi nvictor! :smile:

(have a theta: θ and a pi: π and use bold for vectors :wink:)
nvictor said:
show that when the x component of the displacement of one of the particles is 2 * Pi * (m / qB) * vcos(theta), where theta is the angle between v^vector and B^vector, the velocity of the particle is in the same direction as it was when the particle entered the field

The displacement in the x-direction is (vcosθ)t (because speed in that direction is constant), so the question is asking you to prove that the period is 2πm/qB :smile:
 
  • #3
thanks a lot for the reply.
 

1. What is a uniform magnetic field?

A uniform magnetic field is a magnetic field that has the same strength and direction at all points in a given region.

2. How is the direction of a particle affected by a uniform magnetic field?

The direction of a charged particle will be affected by a uniform magnetic field if the particle is moving in a direction that is not parallel or perpendicular to the field. The particle will experience a force perpendicular to both its velocity and the magnetic field, causing it to move in a curved path.

3. Can the direction of a particle change in a uniform magnetic field?

Yes, the direction of a particle can change in a uniform magnetic field if the particle is moving in a direction that is not parallel or perpendicular to the field. The particle will experience a force that causes it to move in a curved path, resulting in a change in its direction.

4. How can the direction of a particle in a uniform magnetic field be calculated?

The direction of a particle in a uniform magnetic field can be calculated using the right-hand rule. This rule states that if the thumb of your right hand points in the direction of the particle's velocity, and your fingers point in the direction of the magnetic field, then the direction of the particle's path will be perpendicular to both.

5. What factors can affect the direction of a particle in a uniform magnetic field?

The direction of a particle in a uniform magnetic field can be affected by the strength and direction of the magnetic field, the charge and velocity of the particle, and the mass of the particle. Additionally, the presence of any other magnetic or electric fields in the region can also influence the direction of the particle.

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