Magnetic Field and Magnetic Force

[ihearyourecho]

Homework Statement

A positively charged particle moves through a region with a uniform electric field pointing into the page and a uniform magnetic field pointing toward the top of the page. The particle can have one of the four velocities shown in the figure .

http://session.masteringphysics.com/problemAsset/1126298/2/5416322074_76.jpg

A) Rank the four possibilities in order of decreasing magnitude of the net force (F1, F2, F3, and F4) the particle experiences.
Rank forces from largest to smallest.

B) Which of the four velocities could potentially result in zero net force?

Homework Equations

F=qvBsin(theta_

The Attempt at a Solution

WELL, in the equation F=qvBsin(theta), q, V, and B are negligible. Therefore, all the magnitude depends on in this case is the angle. Since the force is 0 if the velocity is parallel to the magnetic field, I thought V₂ and V₄ would be 0 and V₁ and V₃ would be a larger magnitude. This isn't the right answer though. Once I figure out part A, I should be able to do Part B. Where in my thinking was my logic flawed?

Thanks!

 

[ehild]

You did not count the electric field.

ehild

 

[ihearyourecho]

Where does the electric field come into play? It's not in the equation, is it? Or am I using the wrong equation...?

 

[Doc Al]

Where does the electric field come into play?

You have a charged particle in an electric field.

It's not in the equation, is it? Or am I using the wrong equation...?

You are only using 'half' of the correct equation. You need the full Lorentz force, which includes an electric force component as well as the magnetic force. Both fields exert their own force.

 

[ihearyourecho]

Err, we've never done "Lorentz force"

 

[Doc Al]

Err, we've never done "Lorentz force"

But you've done electric fields and forces, I hope.

"Lorentz force" is just the name for both electric and magnet forces combined: http://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.html"

 

[ihearyourecho]

Hmm, I guess we've just never done a problem like this before.
So F=qE + qvBsin(theta)

Since the Electric field is the same for all the forces, I'm still not sure how it applies.. Wouldn't it be the same as having a constant velocity for all of them, negligible?

I'm not trying to get you to do this for me, I just don't understand since I haven't seen something like this before

 

[Doc Al]

Since the Electric field is the same for all the forces, I'm still not sure how it applies.. Wouldn't it be the same as having a constant velocity for all of them, negligible?

The electric force will be the same in all cases. But that force is a vector and must be added to the magnetic force vector, which is different in each case, to get the net force.

Hint: Consider the relative directions of those two force vectors.

 

[ihearyourecho]

In my thinking, that still doesn't help

F=qE+qvBsin(theta)

F1=qE (Into the Page) + qvBsin(90) (Right along x axis)
F2=qE (Into the Page) + qvBsin(0) = qE (Into the Page) + 0 = qE (Into the Page)
F3=qE (Into the Page) + qvBsin(90) (Left along x axis)
F4=qE (Into the Page) +qvBsin(0) = qE (Into the Page) + 0 = qE (Into the Page)

In my mind, F1 and F3 still have the same magnitude, and that magnitude is greater than that of F2 and F4, which have the magnitude of simply qE

 

[Doc Al]

F1=qE (Into the Page) + qvBsin(90) (Right along x axis)
F2=qE (Into the Page) + qvBsin(0) = qE (Into the Page) + 0 = qE (Into the Page)
F3=qE (Into the Page) + qvBsin(90) (Left along x axis)
F4=qE (Into the Page) +qvBsin(0) = qE (Into the Page) + 0 = qE (Into the Page)

How are you determining the direction of the magnetic force? Hint: You need the right hand rule.

 

[ihearyourecho]

Why does the direction of the magnetic force matter if we're just trying to find the magnitude of it?

EDIT: Nevermind, one moment please

 

[ihearyourecho]

Okay, I got the right answer. I guess it all makes sense in retrospect, but I was totally lost throughout the whole thing until that last little bit of advice.

Thanks for your help man.