Motion of a charged particle in magnetic field

[Abhimessi10]

Homework Statement

A particle of charge -q and mass m enterd magnetic field B at A with speed v1 at an angle alpha and leaves the field at C with v2 at angle beta.Then,

a)alpha=beta
b)v1=v2
c)particle remains in the field for time t=(2m(pi-alpha))/qB
d)All of these

Please see image below

https://ibb.co/iLMrie

Homework Equations

F=qvB

The Attempt at a Solution

Really don't know how to do it.Tried resolving components.

 

[kuruman]

Homework Statement

A particle of charge -q and mass m enterd magnetic field B at A with speed v1 at an angle alpha and leaves the field at C with v2 at angle beta.Then,

a)alpha=beta
b)v1=v2
c)particle remains in the field for time t=(2m(pi-alpha))/qB
d)All of these

Please see image below

https://ibb.co/iLMrie

Homework Equations

F=qvB

The Attempt at a Solution

Really don't know how to do it.Tried resolving components.[/B]

Resolving components will not get you very far. Other than F=qvB, what else do you know about the motion of particles in magnetic fields? Can you draw the path connecting the entry and exit points of the particle?

 

[berkeman]

F=qvB

Are you familiar yet with the vector form of that equation (the Lorentz force)? Thinking about the problem in terms of vectors is a lot easier and more intuitive, IMO.

http://www.assignmentpoint.com/wp-content/uploads/2017/05/Lorentz-Force0.jpg

 

[Abhimessi10]

Are you familiar yet with the vector form of that equation (the Lorentz force)? Thinking about the problem in terms of vectors is a lot easier and more intuitive, IMO.

http://www.assignmentpoint.com/wp-content/uploads/2017/05/Lorentz-Force0.jpg

View attachment 231365

Yeah i am.

 

[Abhimessi10]

Resolving components will not get you very far. Other than F=qvB, what else do you know about the motion of particles in magnetic fields? Can you draw the path connecting the entry and exit points of the particle?

I don't know to draw the path for particles entering at general angles.just the case when angle=90, 0, and in between.

 

[kuruman]

I don't know to draw the path for particles entering at general angles.just the case when angle=90, 0, and in between.

OK. What kind of path do you get in these cases? Why is the path like that and like something else?

 

[Abhimessi10]

OK. What kind of path do you get in these cases? Why is the path like that and like something else?

Because of magnetic force acting as centripetal force?

 

[kuruman]

Because of magnetic force acting as centripetal force?

Yes., and if the magnetic force is centripetal, what kind of path does the particle describe for as long as the force remains centripetal?

 

[Abhimessi10]

Yes., and if the magnetic force is centripetal, what kind of path does the particle describe for as long as the force remains centripetal?

Depends on the angle velocity makes with the magnetic field.On a general basis i can say circular-kinda motion.

 

[kuruman]

Depends on the angle velocity makes with the magnetic field.On a general basis i can say circular-kinda motion.

Look at your drawing. The magnetic field is directed into the screen and the velocity vector is in the plane of the screen. What do you think the angle between the magnetic field and the velocity is?

 

[Abhimessi10]

Look at your drawing. The magnetic field is directed into the screen and the velocity vector is in the plane of the screen. What do you think the angle between the magnetic field and the velocity is?

The sin alpha component of velocity is only perpendicular
and cos alpha would remain same?

 

[kuruman]

The sin alpha component of velocity is only perpendicular

Imagine placing your index finger perpendicular to the face of an analog clock and keeping it fixed. What is the angle between your finger and the seconds hand at any time t? The seconds hand is like the velocity vector that changes direction in the plane of the screen and your index finger is like the magnetic field the direction of which is fixed.