# What direction is current for an electron in both $E$ and $B$ fields?

According to Fleming's left hand rule:

I am a bit confused however in the case of an electron travelling in a region of both electric and magnetic fields, which direction would the electric current be?

I know that for a current carrying conductor, the current is opposite to electron flow, does that mean that in the case of a single electron the current would be in the opposite direction to the motion of the electron?

• In your text you write "Fleming's left hand rule", but your image shows a right hand.. Commented Dec 5, 2020 at 11:29

No matter what fields exist in space, electric current is always in the direction opposite to the direction of motion of e-, because e- are negatively charged particles.

However, current is not defined for a single e-, because current is a continuous flow of charges. But if we have to tell the direction of current anyways in case of a single e-, we would say it is in the opposite direction.

In the image attached, electric current means that if a positively charged particle is moving in that direction, B is in that direction, then Force will be in this direction.

If an e- is moving in the same direction as the positively charged particle was moving, then direction of force will rotate 180 degs

• Not sure why you assume that electric current arises necessarily from electrons (what about ions? positrons? quasielectrons?). Commented Dec 5, 2020 at 12:31

Fleming's right hand rule (as shown in your image) is just a mnemonic for the cross product in the formula $$F=I\vec{\ell}\times\vec{B}$$ where $$\vec{F}$$ is the magnetic force acting on a piece of wire, $$I$$ is the current, $$\vec{\ell}$$ is the length of the piece of wire, and $$\vec{B}$$ is the magnetic field.

This magnetic force on a current-carrying wire is actually a consequence of the Lorentz forces acting on all the electrons moving within the wire.

The Lorentz force on a single particle is $$\vec{F}=q\vec{v}\times\vec{B}$$ where $$q$$ is the electric charge and $$\vec{v}$$ is the velocity of the particle.

Remember that an electron is negatively charged (i.e. $$q$$ is negative) and therefore its velocity is opposite to the direction of the current.

So therefore you can use the same right hand rule for ($$\vec{F}, q\vec{v}, \vec{B}$$) like you did for ($$\vec{F}, I\vec{\ell}, \vec{B}$$).