force, magnetic field, current, long straight wire

jaredmt

1. The problem statement, all variables and given/known data
A long, straight wire carries a current of 2.5 A. An electron is traveling in the vicinity of the wire. At the instant when the electron is 4.5cm from the wire and traveling with a speed of 6.00 X 10^4 m/s directly toward the wire, what are the magnitude and direction (relative to the direction of the current) of the force that the magnetic field of the current exerts on the electron?


2. Relevant equations
F = qv X B

for an infinitely long straight wire:
B = (2x10^-7)(I)/r

so...
F = (qv) X (2x10^-7)(I)/r

3. The attempt at a solution
I = 2.5A
r = .045m
v = 6x10^4 m/s
q = -1.6X10^-19 C


The answer is F = 1.07 X 10^-19 N. i got that right. but how do i know whether it is going with the current or against the current?

i think all i know is magnetic field, current and direction of electron are all perpendicular to each other. The answer says it goes WITH the current, but i dont understand how they got that

gabbagabbahey

Use the right hand rule: (1) point your fingers in the oppsosite direction of motion of the electron (since the electron has negative charge, qv will point opposite to v),(2) then curl them in the direction of the magnetic field; your thumb will then point in the direction of the force.

jaredmt

ok but first i would have to get the direction of the magnetic field. im trying to see this with vector equations (i'd probably screw up the right hand rule on a test). i tried 2 different vector equations, 1 with the current in positive direction and 1 with the current in negative direction. let me know if this looks right:
B = magnetic field
r = distance from wire
q = charge
F = force

1)
B = IlXr

I(j) X r(i) = B(-k)

F = qv X B = -q(-i) X B(-k) = F(j)


2)
B = Ilxr
I(-j) X r(i) = B(k)

F = qv X B = -q(-i) X B(k) = F(-j)


the answers match up and im pretty sure i did it right but i'd feel more confident if some1 could verify this

gabbagabbahey

Looks good to me

However, I recommend you get a little practice with the right hand rule too. It can save you a lot of time on an exam.

In addition to finding the direction of the force (using the method I gave above), the right-hand rule can also help you find the direction of the magnetic field (which you of course need to know in order to find the force). Just point your thumb in the direction of the current, and make a loose fist....your fingers will curl around in the direction of the field.