Simple magnetic field circular motion problem

In summary, when a beam of protons is moving at a 30 degree angle from the +x-axis in the x-y plane with a magnetic field oriented in the +z-axis, the particle's motion would be helical. This is because the velocity is not completely perpendicular to the field. If the velocity were at a 90 degree angle, the motion would be circular since it would still be perpendicular to the magnetic field.
  • #1
letsgo
20
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There's basically a beam of protons moving in the x-y plane, 30 degree from the +x-axis. The magnetic field is oriented in the +z-axis. So would the particle's motion be circular or helical?

I say helical, because the velocity isn't completely perpendicular.
Is this correct?
 
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  • #2
If the velocity is not perpendicular to the field, what angle to you think it makes, and why?
 
  • #3
Okay, is it 90? So then it means it is circular? Since even though its 30 degrees from the x-axis, its still perpendicular to the B-field?
 
  • #4
letsgo said:
Okay, is it 90? So then it means it is circular? Since even though its 30 degrees from the x-axis, its still perpendicular to the B-field?
Yes, it should describe a circle in the XY plane.
 
  • #5


Yes, you are correct. The particle's motion would be helical because the velocity has a component in the z-direction due to the 30-degree angle from the +x-axis. This means that the force from the magnetic field will cause the particle to move in a circular path in the x-y plane, but also simultaneously in the z-direction, resulting in a helical motion. This is known as a helical trajectory and is commonly observed in charged particle motion in a magnetic field.
 

1. What is a simple magnetic field circular motion problem?

A simple magnetic field circular motion problem is a physics problem that involves a charged particle moving in a circular path due to the influence of a magnetic field. The direction and magnitude of the magnetic field, as well as the properties of the charged particle, are typically given in the problem.

2. How do you determine the direction of the magnetic field in a simple magnetic field circular motion problem?

The direction of the magnetic field in a simple magnetic field circular motion problem can be determined using the right-hand rule. Point your thumb in the direction of the particle's velocity, and curl your fingers in the direction of the magnetic field. The direction your fingers are pointing is the direction of the magnetic field.

3. What is the equation for the force on a charged particle in a simple magnetic field circular motion problem?

The equation for the force on a charged particle in a simple magnetic field circular motion problem is F = qvB, where q is the charge of the particle, v is the velocity, and B is the magnetic field strength. This force is always perpendicular to both the velocity and the magnetic field.

4. How does the radius of the circular path in a simple magnetic field circular motion problem change with the velocity of the particle?

The radius of the circular path in a simple magnetic field circular motion problem is directly proportional to the velocity of the particle. This means that as the velocity increases, the radius of the path also increases. This can be seen in the equation for centripetal force, F = mv^2/r, where r is the radius.

5. Can a charged particle have circular motion in a uniform magnetic field?

Yes, a charged particle can have circular motion in a uniform magnetic field. This occurs when the magnetic field is perpendicular to the velocity of the particle. The force exerted by the magnetic field causes the particle to continuously change direction, resulting in circular motion.

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