Motion of a particle in a uniform magnetic field

[Physics lover]

Homework Statement

A uniform magnetic field exists given by B=b k^ . A particle of mass m and charge q is present in magnetic field has an initial velocity v=v (i^+j^+k^). Find the particle's position and velocity after t seconds.

All i could think is that the z component of velocity will remain unchnged as there is no force in that direction.And for the x and y component can we imagine the helical motion as a superposition of a circle and a straight line.So for x and y component can we solve for a particle moving in a circular path.

Relevant Equations

F=qVBsintheta
Radius=mV/qB

All i could think is that the z component of velocity will remain unchnged as there is no force in that direction.And for the x and y component can we imagine the helical motion as a superposition of a circle and a straight line.So for x and y component can we solve for a particle moving in a circular path.

 

[scottdave]

I believe the correct formula for Radius=mV/(qB). You are correct that the magnetic field will not have a force in the k direction, so you need to figure out the portion of v which is responsible for the resultant force.

 

[Physics lover]

I believe the correct formula for Radius=mV/(qB). You are correct that the magnetic field will not have a force in the k direction, so you need to figure out the portion of v which is responsible for the resultant force.

I think they are i and j components.

 

[haruspex]

Problem Statement: A uniform magnetic field exists given by B=b k^ . A particle of mass m and charge q is present in magnetic field has an initial velocity v=v (i^+j^+k^). Find the particle's position and velocity after t seconds.

All i could think is that the z component of velocity will remain unchnged as there is no force in that direction.And for the x and y component can we imagine the helical motion as a superposition of a circle and a straight line.So for x and y component can we solve for a particle moving in a circular path.
Relevant Equations: F=qVBsintheta
Radius=mV/qB

for x and y component can we solve for a particle moving in a circular path.

Yes. I don't see an initial position specified. Is it the origin?
What do you get for the x and y displacements after time t?

 

[Physics lover]

Yes. I don't see an initial position specified. Is it the origin?
What do you get for the x and y displacements after time t?

There is no specified position in the question.I think the particle wil be on the middle of quarter circumference of the circle in the 2nd quadrant.Because then only the direction of force will be pointing towards origin.

 

[haruspex]

There is no specified position in the question.I think the particle wil be on the middle of quarter circumference of the circle in the 2nd quadrant.Because then only the direction of force will be pointing towards origin.

Wherever the particle starts it will describe an identical helix, just shifted in the XY plane.