# Current through a wire and electron deflection

1. Apr 22, 2008

### oh.rry21

so i know this is a classical experiment but im having trouble understanding this idea.

basically the experiment shoots an electron at a current charged wire (current coming "out of the page"). Does increasing/decreasing the current change the trajectory of the electron. and if so/if not, why?

im guessing that changing current will change the trajectory of the electron because of the fact that a changing current induces a magnetic field that exerts a force on the moving electron? but at the same time i read somewhere that it never does "work" on the electron. any ideas? :(

2. Apr 22, 2008

### Nick89

Technically it's not a changing current that induces a magnetic field. A fixed, constant current also induces a magnetic field. It's moving charge(s) that induce the magnetic field.
A change in the magnetic field however will induce a current (or electric field).

If the current gets larger however, the magnetic field around the wire will also get larger:
$$B = \frac{\mu_0 I}{2 \pi r}$$

The trajectory of the electron is determined by the Lorentz force:
$$\vec{F_l} = q \vec{v} \times \vec{B}$$

How does the electron get fired at the wire? In what direction?
You might see from the formula for the lorentz force that if the direction of the moving electron (direction of v) is the same as the direction of the magnetic field (B) than the cross-product will be 0 so the field will exert no force on the electron.

Since the magnetic field will be circling around the wire however, it is important how the electron is moving in relation to the wire (parallel to the wire, at a right angle to the wire etc..?)

3. Apr 22, 2008

### oh.rry21

well if the current carrying wire is going "out of the page" (negative Z direction?) then the electron would be travelling along the (negative X axis) to be supposedly deflected downward into the negative Y direction

is that the same direction as the direction of the magnetic field then?

4. Apr 22, 2008

### Nick89

Using the right-hand rule you can determine the direction of the magnetic field.

Point your thumb (right hand) in the direction of the current (in this case, up), then your other fingers will indicate the direction of the magnetic field.

In this case, the magnetic field will be circeling around the wire counter-clockwise (or in the $$\vec{e_{\phi}}$$ direction).

See the image:
i29.tinypic.com/4l26q0.jpg

If the electron (e) is moving toward the wire (the right-most electron in the image) then the magnetic field B will point at a perpendicular angle to the line from the wire to the electron. Since the electron's speed v is in the -x direction and the magnetic field B has a component in the +y direction, the cross-product for the lorentz force yields a force in the -z direction.

If the electron is moving away from the wire (left-most electron) then the magnetic field will have a component in the -y direction, so the cross-product yields a force in the +z direction.

If the electron is on the y-axis (in the image) than the magnetic field vector and the speed vector will point in the same (but opposite) direction, yielding NO force.

Looking 'from the side' you will see the electron make like a bend. The lorentz force will not act in the x or y direction so from the top-view (looking down the z-axis) you will see a straight line.

However, this does seem strange to me... I don't know why... I never encountered such a problem with an electron and a wire. I only ever saw these problems with uniform magnetic fields...
I might be doing something wrong, but I don't think so though.

What makes you think the electron gets a deflection in the negative y-direction? This cannot happen since both the magnetic field and the electron's speed vectors lie in the xy-plane. The lorentz force is always perpendicular to both the speed and magnetic field so the lorentz force can never lie in the xy-plane aswell. It should always be in the + or -z direction.

Last edited: Apr 22, 2008