What would be the magnetic force on the arm? This is a hard one!?

Question

Sodium ions (Na+) move at 0.794 m/s through a bloodstream in the arm of a person standing near a large magnet. The magnetic field has a strength of 0.26T and makes an angle 70.3 degrees with the motion of the sodium ions. The arm contains 74.8cm3 of blood, (within the magnetic field) with 1.61 x 10^20 Na/cm3. If no other ions were present in the arm, what would be the magnetic force of the arm? Answer in units of N.

Answer 1

Well I sorta agree with bob shark.

But suppose you somehow got the Na+ to run thru the blood without the neutalizing ion CL- or whatever. Still I say no magnetic force because the blood has to make the return trip. The "electric current" of the arterial flow will be cancelled by the "current" of the (what's it called?) veinous flow. No net current, no magnetic interaction.

Answer 2

We can treat sodium ions in the arm as the electric current and the arm as the wire, so we can use the equation for the magnetic force on the current wire:
Fm = i L x B (this is the cross product of vector L and vector B)
so the magnitude of the force is:
Fm = iLB sin θ, where θ is the angle between the vector L which has the direction of the velocity of the ions, and the magnetic field vector.
We know B = 0.26 T and θ = 70.3°, we must get I and L.
The current of the ions is i = q/t = Ne/t, where N is the number of the ions that pass and e is the elementary charge.
We don't know N, but we have the number density n = N/V = 1.61 x 10^20 ions/cm3 and the volume of the blood within the magnetic field, so N = nV. This yields i = nVe/t. If we subsitute this into the equation for the magnetic force, we get:
Fm = nVe/t x LB sin θ. The length of the "wire" is the length of the arm L, which can be written as L = vt and we finally have the force:
Fm = nVev x B sin θ (t is cancelled out of the equation)
So:
Fm = 1.61 x 10^20 /cm3 x 74.8 cm3 x 1.602 x 10^─19 As x 0.794 m/s x 0.26 N/Am x sin 70.3° = 375 N

Answer 3

There would be no magnetic attraction of the arm to the magnet as there is nothing in the arm or blood that would be attracted by the magnet