At a Particular Instant an Electron Is Traveling in the +x Direction, With Speed 4105 M/s.

jaredmt

Homework Statement

A long, directly 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 ten^4 m/s directly toward the wire, what are the magnitude and direction (relative to the management of the current) of the force that the magnetic field of the electric current exerts on the electron?

Homework Equations

F = qv X B

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

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

The Effort at a Solution

I = 2.5A
r = .045m
five = 6x10^4 m/s
q = -1.6X10^-19 C

The reply is F = 1.07 X x^-19 Due north. i got that right. merely how do i know whether information technology 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 information technology goes WITH the current, but i dont understand how they got that

gabbagabbahey

Utilize the right hand rule: (one) 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 volition and then point in the direction of the force.

jaredmt

ok only first i would take to get the direction of the magnetic field. im trying to meet this with vector equations (i'd probably spiral up the right manus dominion on a exam). i tried 2 different vector equations, 1 with the electric current in positive management and 1 with the electric current in negative management. permit me know if this looks right:
B = magnetic field
r = altitude from wire
q = accuse
F = forcefulness

1)
B = IlXr

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

F = qv X B = -q(-i) X B(-1000) = F(j)

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

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

the answers friction match up and im pretty certain i did it correct simply i'd experience more confident if some1 could verify this

gabbagabbahey

Looks skilful to me :approve:

Yet, I recommend you get a petty practice with the right paw dominion too. Information technology can save you a lot of fourth dimension on an exam.

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

At a Particular Instant an Electron Is Traveling in the +x Direction, With Speed 4105 M/s.