How Do You Calculate Magnetic Energy Density at an Atom's Center?

[phyvamp]

Homework Statement

In an atom: suppose one electron orbits the n proton nucleus at radius r . Find the magnetic energy density, in J/m3, at the center of the atom due to the motion of this electron.

NOTE: You can ignore the effect of other electrons in this atom.

Homework Equations

u=B^2/2*u_o
= (N*u_o*I)^2 /2u_o
or=N*(u_o*I)^2 /2u_o

The Attempt at a Solution

1)
Is the number of protons can be treat as the number of turns of the magnetic field, should I plug N inside the parentheses

2)
Since qvB=IBL and I get I=qv/L, and then I use mv^2/r = kqq/r^2 to get the expression of v and plug it in qv/L and finally plug the expression of I in the (N*u_o*I)^2 /2u_o.
Am I on the right track or it is completely wrong?

 

[rude man]

I am not sure what you were trying to do. Looks like you are trying to use Ampere's law but this is not applicable here.
I suggest:
1. find B at the center of the atom. This involves finding the speed of the rotating electron as it circles around the N-proton nucleus. You now have a curren loop of known parameters (i and r) centered on the nucleus.
2. Use Biot-Savart (or your textbook, probably) to determine B at the nucleus.
3. Use your formula for energy density.

 

[phyvamp]

I am not sure what you were trying to do. Looks like you are trying to use Ampere's law but this is not applicable here.
I suggest:
1. find B at the center of the atom. This involves finding the speed of the rotating electron as it circles around the N-proton nucleus. You now have a curren loop of known parameters (i and r) centered on the nucleus.
2. Use Biot-Savart (or your textbook, probably) to determine B at the nucleus.
3. Use your formula for energy density.

Thank you for the reply. And Yes, I was trying to use Ampere's law. But why it is not applicable here? I though electron is moving in a circular path, so it supposes to be symmetrical? And when you said "You now have a current loop of known parameters (i and r) centered on the nucleus", how do I know the current?

 

[rude man]

While Ampere's law is valid for any closed path pierced by the loop, the B field around it is not at all constant, so you cannot say that ∫B dl = B 2πr even though ∫B dl = μi is correct. So you can't evaluate B at any point around your path. Also, why did you include N in the Ampere formula?

Figure out what the speed of the orbiting electron is around the loop. Then i = dq/dt at any point on the electron's orbit.

 

[kerlos]

can someone show work for this problem please

 

[kerlos]

While Ampere's law is valid for any closed path pierced by the loop, the B field around it is not at all constant, so you cannot say that ∫B dl = B 2πr even though ∫B dl = μi is correct. So you can't evaluate B at any point around your path. Also, why did you include N in the Ampere formula?

Figure out what the speed of the orbiting electron is around the loop. Then i = dq/dt at any point on the electron's orbit.

can u please show work ?

 

[rude man]

can u please show work ?

No, as The Prisoner (old TV show) was told, "That would be telling".