Register to reply

Relationship between force and Velocity in Magnetic Fields

by Typhon4ever
Tags: fields, force, magnetic, relationship, velocity
Share this thread:
Typhon4ever
#1
Apr17-13, 10:07 PM
P: 43
A negative particle is moving in a uniform magnetic field pointing in the negative k direction. The force on the particle is -i and j. Find the x and y components of velocity. (I left out the numerical data in the question). I used F=q*v*B and in order to find the x component I used the F in the x direction with is wrong. You need to use the F in the y direction to find x component. Why?
Phys.Org News Partner Physics news on Phys.org
Symphony of nanoplasmonic and optical resonators produces laser-like light emission
Do we live in a 2-D hologram? New Fermilab experiment will test the nature of the universe
Duality principle is 'safe and sound': Researchers clear up apparent violation of wave-particle duality
jedishrfu
#2
Apr17-13, 10:30 PM
P: 2,969
The force on a charged particle acts perpendicular to the direction of travel and the B field following right hand rule for cross products of vectors:

F = q(E + v x B) where F, E and B are vector quantities and x means cross product.
Typhon4ever
#3
Apr17-13, 10:35 PM
P: 43
Quote Quote by jedishrfu View Post
The force on a charged particle acts perpendicular to the direction of travel and the B field following right hand rule for cross products of vectors:

F = q(E + v x B) where F, E and B are vector quantities and x means cross product.
I thought that the F that is perpendicular to the velocity is the scalar quantitity and we need to decompose it into x and y vectors quantities and use the F in these x and y directions to find the corresponding x and y velocities.

jedishrfu
#4
Apr17-13, 11:10 PM
P: 2,969
Relationship between force and Velocity in Magnetic Fields

Quote Quote by Typhon4ever View Post
I thought that the F that is perpendicular to the velocity is the scalar quantitity and we need to decompose it into x and y vectors quantities and use the F in these x and y directions to find the corresponding x and y velocities.
True F is perpendicular to the v but it is also perpendicular to the B. the equation you wrote F=qvB
gives the magnitude of F.
Typhon4ever
#5
Apr17-13, 11:15 PM
P: 43
I'm confused. If there is a force in the -i direction on the particle as well as a force in the j direction and we want the i and j velocities why don't we just use the corresponding forces in the corresponding directions? A force in the -i direction will affect the i velocity won't it?
Typhon4ever
#6
Apr17-13, 11:30 PM
P: 43
Hmm. I was using F=qvB sin(theta) but I don't know sin(theta). I should have used F=qv x B because I know then that F is perpendicular to v so I must choose the perpendicular force. Correct? Or are you still able to use the angle version.
Simon Bridge
#7
Apr18-13, 12:32 AM
Homework
Sci Advisor
HW Helper
Thanks
Simon Bridge's Avatar
P: 12,870
Quote Quote by Typhon4ever View Post
Hmm. I was using F=qvB sin(theta) but I don't know sin(theta). I should have used F=qv x B because I know then that F is perpendicular to v so I must choose the perpendicular force. Correct? Or are you still able to use the angle version.
Geometrically, the force is perpendicular to both the velocity and the magnetic field. The relationship is written mathematically as a vector cross product - so that is what you should use.

There are lots of ways to evaluate the cross product - |u x v| = |u||v|sinθ is one of them.
However, this relation only computes the magnitudes, the question is asking about directions.

If you put the magnitudes equal to 1 for each vector you can find sinθ - but it is more convenient to evaluate the vector cross product directly.

It is even easier to do it using the right-hand rule.
Typhon4ever
#8
Apr18-13, 02:23 AM
P: 43
Quote Quote by Simon Bridge View Post
Geometrically, the force is perpendicular to both the velocity and the magnetic field. The relationship is written mathematically as a vector cross product - so that is what you should use.

There are lots of ways to evaluate the cross product - |u x v| = |u||v|sinθ is one of them.
However, this relation only computes the magnitudes, the question is asking about directions.

If you put the magnitudes equal to 1 for each vector you can find sinθ - but it is more convenient to evaluate the vector cross product directly.

It is even easier to do it using the right-hand rule.
I'm not sure what you mean by putting the magnitudes equal to 1. How exactly do you find sin theta that way?
Simon Bridge
#9
Apr18-13, 02:37 AM
Homework
Sci Advisor
HW Helper
Thanks
Simon Bridge's Avatar
P: 12,870
I misspoke ... my apologies.
I got confused because you have not provided all the information given to you about the problem.
You appear to have given us the force direction and magnitude, the magnetic field direction only, and only the sign of the charge.

I assumed which more information was available to you without checking first.
Typhon4ever
#10
Apr18-13, 02:45 AM
P: 43
ok to be specific the charge is -5.00 nC, B=-(1.28T)k, Magnetic F= -(3.3010^-7 N)i+(7.6010^−7 N)j. Does that change anything?
Simon Bridge
#11
Apr18-13, 03:10 AM
Homework
Sci Advisor
HW Helper
Thanks
Simon Bridge's Avatar
P: 12,870
That changes the magnitude and direction of the force for starters... which changes the plane that the velocity is in. But it confirms what I thought - you have to do the vector math.

rewriting as vectors... $$\vec{F}=\begin{pmatrix}-3.30\\7.60\\0\end{pmatrix}\times 10^{-7}\text{N} \; ;\;
\vec{B} = \begin{pmatrix}0\\0\\-1.28\end{pmatrix}\text{T}\; ;\; \vec{v}=\begin{pmatrix}v_x\\v_y\\v_z\end{pmatrix}\text{m/s}\; ;\; q=-5.00\times 10^{-9}\text{C}\\
\vec{F}=q\vec{v}\times\vec{B}$$... do you know how to do a cross product?

Note - you can only find the x and y components of the velocity.
Fortunately, that is all they ask for.


Register to reply

Related Discussions
Relationship between the pulling force and the magnetic field of a magnet General Physics 2
Charges moving parallel to magnetic fields and direction of magnetic force Classical Physics 2
What Is The Relationship Between Temperature and Magnetic Force? General Physics 4
Force of an electron with magnetic and electric fields and velocity Introductory Physics Homework 3
Current in relation to magnetic fields and velocity Introductory Physics Homework 1