Question

An electron is traveling above a long wire which has zero current; the figure below shows a
view from the side. The current is then switched on to travel to the right in the plane of the page.
What will be the direction of the electron’s deflection once the current is on?http://i.imgur.com/E8dBgoa.png
Out of the page, towards the wire, away from the wire, into the page, or the electron won't deflect?

Answer 1

Okay, just remember your right hand rules here. Right hand rule for ANY cross product is

thumb points in the direction of the first vector
pointer points in the direction of the second vector
curl your middle finger at the first knuckle (where it connects to your hand) and it points in the direction of the resultant vector.

Right hand rule for the magnetic field of a current carrying wire is

Thumb points in the direction of current
The rest of your fingers curl around in the direction of the magnetic field (so the magnetic field is basically wrapping around the wire.

Okay, now we want to look at the equation so we know how the electron will be deflected. Equation for magnetic force is: \[F_m = qv \times B\] where
q = charge of the particle
v = velocity of the particle in the magnetic field
B = strength of the magnetic field. (B-field = magnetic field as an abbreviation)

Now we can ignore q since we are only interested in direction. We know the direction of the velocity of the electron. And we know the direction of current through the wire so we can find the direction of the B-field by pointing our right thumb in the direction of the current and curling our fingers into a loose fist. You should get that the B-field at the electron is pointing out of the page/screen.

Now, right hand rule for cross-products to find the direction of the deflection:
Our cross product is: \[F_m = qv \times B\]So the first vector is the velocity 'v'. So our right thumb points in the direction of the velocity (right).
Second vector is the magnetic field 'B'. So our pointer finger points in the direction of the B-field (out of the page)
So the resultant vector points in the direction of our middle finger bent at the the first knuckle only (so down).

So the electron will be deflected towards the wire. Hope you understood all that! Good Luck!

Answer 2

nice explanation, but you have left out the negative charge on the electron. because of the negative charge, the direction of deflection will be away from the wire.

Answer 3

Oh doh! You're right. Gotta watch those little details. Thanks for catching that.