Acceleration of an Electron in Earth's Magnetic Field

[chrisfnet]

Homework Statement

Earth's magnetic field near the equator is 5.0x10^-5 T due north. Find the acceleration of an electron traveling northeast at 2.0x10⁵ m/s. The charge on an electron is -1.602x10^-19 C and it's mass is 9.109x10^-31 kg.

Homework Equations

Fm = |q|vB*sin(theta)

a = Fm/m

The Attempt at a Solution

Fm = |-1.602x10^-19C|*2.0x10⁵m/s*5.0x10^-5T*sin(45)
Fm = 1.13x10^-18N

a = Fm/m = 1.13x10^-18N/9.109x10^-31kg = 1.24x10¹²m/s²

For some reason, I lost 1 point on this problem. I'm not sure where, how or why...

Should the acceleration also have a direction? If so, what would that be? Thank you for any input...

 

[Hellabyte]

Yes, acceleration is a vector so it must be specified with a direction. By Newtons second law we can see that the acceleration is in the same direction of the force.

A charged particle moving in a magnetic field has a force on it that has a direction shown by the right hand rule.

http://en.wikipedia.org/wiki/Right-hand_rule

hold out your right hand and put your fingers in the following orientation with your fingers in the direction of your vectors.

pointer finger-> velocity of a charged particle.
middle finger -> direction of the B field

and whatever direction your thumb points is the direction of your force, and acceleration.

 

[collinsmark]

I'm guessing you lost the 1 point because you didn't specify the direction of acceleration (which is the direction of the force).

You can find the direction of the force vector using the right hand rule.

(Note: not only is the resulting force a vector, but the electron's velocity is a vector, and the magnetic field is a vector too. The right hand rule can help you find the direction of any one, given the direction of the other two. You just need to remember which parts of your hand go with which vectors.)

(Extra special note: The negative sign on the electron's charge fits into the result too, so don't forget about that.)

 

[Hellabyte]

Oh yeah woops, forgot about that whole negative charge thing too :)

 

[chrisfnet]

So, since it's negatively-charged I use my left hand. This would indicate to me that the acceleration is in the "upward" direction, yes? Should I also indicated "upward" for the force then, also?

 

[Hellabyte]

yes exactly.

 

[collinsmark]

Wait, I think you have it backwards.

Perhaps the confusion is that the Earth's magnetic South pole is near the Earth's true North pole (and vise versa). This means that the magnetic field lines on the surface of the Earth generally point North (as in generally toward the true North pole). This is also consistent with the problem statement, "Earth's magnetic field near the equator is 5.0x10-5 T due north..."

Try the rule again, making sure the magnetic field is pointing North.

 

[Hellabyte]

Oh my bad. That was definitely stupid of me. not like i was trying to sound like expert or anything.

 

[chrisfnet]

Wait, I think you have it backwards.

Perhaps the confusion is that the Earth's magnetic South pole is near the Earth's true North pole (and vise versa). This means that the magnetic field lines on the surface of the Earth generally point North (as in generally toward the true North pole). This is also consistent with the problem statement, "Earth's magnetic field near the equator is 5.0x10-5 T due north..."

Try the rule again, making sure the magnetic field is pointing North.

It still shouldn't matter...?

Both the magnetic field and the velocity are planar with the surface of the Earth. My thumb is, of course, normal to each which still leaves it.. up?

I'm quite sure my math in this problem is correct and that I just forgot a direction.