Helmholtz Configuration?

Question

I have to derive

B_helmholtz = (8 / 5*sqrt5) (mu_0*N*i / R)

from

B_x (X) = (mu_0 / 2) [NiR^2 / (R^2 + X^2)^3/2]

Now X = R/ 2 and - R/ 2

I'm thinking that you sub this (X) into B_x (X)

Any ideas?

i just can't get it. I think you have to equate the two equations for R/2 and -R/2

Answer 1

You need to start over from the Biot-Savart law and clarify in your head what it means in terms of vector fields, where B_helm is suppose to be determined at, and what its direction is. Starting from an intermediate result that you don't understand the context of will get you nowhere.