Total Particle Energy Flux in Auroral Arcs

[DaynaClarke]

Homework Statement

Consider electron precipitating vertically into an auroral arc of area 1.0 km x 1200 km in the horizontal plane. The energy of the electrons is equal to 5 keV and the electron flux is $$8.0 x 10^13 m^-2 s^-1$$.
Determine the total particle energy into the arc, the total current flowing, and the direction of this current.

Relevant Equations

Electron flux = rate of flow of electrons per unit area
Current = rate of flow of electrons

Homework Statement: Consider electron precipitating vertically into an auroral arc of area 1.0 km x 1200 km in the horizontal plane. The energy of the electrons is equal to 5 keV and the electron flux is 8.0 x 10^13 m^-2 s^-1.
Determine the total particle energy into the arc, the total current flowing, and the direction of this current.
Homework Equations: Electron flux = rate of flow of electrons per unit area
Current = rate of flow of electrons

So, I have this question on a past paper which I'm doing for revision, but I have no answers to see if I'm right or on the right track.

So far, I have the total particle energy flux as 4\times 10^{17} eVm^{-2}s^{-1}. I got this by multiplying the energy of the electrons by the electron flux. But this seems far too simple?

Current is the rate of flow of electrons, so I did this:
Electron flux * Area = Rate
Rate * Electron Charge = Current
It gave me an answer of 15.36 kA. This seems pretty large, but aurorae are large so maybe it isn't too far-fetched?

I have no idea if either of these answers is correct, and I'm also not sure how to work out the direction of the current. I want to say it's the right-hand rule or something, but I don't know.

 

[TSny]

Determine the total particle energy into the arc

This statement is not clear. It could mean to determine the total energy per second that enters the arc. It could mean to calculate the energy flux (as you did), but the word "total" seems to me to imply taking into account the total area of the arc rather than just a unit area.

I think your answer for the current is correct. Regarding the direction of the current, remember that electrons carry a negative charge. If you had a stream of electrons moving to the right, what would be the direction of the current?

 

[DaynaClarke]

This statement is not clear. It could mean to determine the total energy per second that enters the arc. It could mean to calculate the energy flux (as you did), but the word "total" seems to me to imply taking into account the total area of the arc rather than just a unit area.

I think your answer for the current is correct. Regarding the direction of the current, remember that electrons carry a negative charge. If you had a stream of electrons moving to the right, what would be the direction of the current?

Oh, it does say particle energy flux - I must have missed it out whilst transferring the question. Given this, did I calculate it correctly?

So, if electrons have a negative charge and flow to the right, would current flow to the left as my answer is positive? There is a good chance that I'm oversimplifying it.

Thank you for your response!

 

[TSny]

Oh, it does say particle energy flux - I must have missed it out whilst transferring the question. Given this, did I calculate it correctly?

Yes, it's correct.

So, if electrons have a negative charge and flow to the right, would current flow to the left as my answer is positive? There is a good chance that I'm oversimplifying it.

Yes, the current would be to the left. Current is in the direction opposite to the direction the electrons are moving. So, if you know the direction that the electrons are moving into the arc, you can deduce the direction of the current.