In a lab on the current balance of.forces between two parrelel wires with thr cu

Question

In a lab on the current balance of.forces between two parrelel wires with thr current flowing in opposite directions, answer the following question. in the following photo two equations are given: F and Fc.
F is the equation for lorentz law of repulsion force between two wires.
Fc is the wire to wire force in which s is spacing and d is wire diameter. a=s+d. Please explain why even though the two equations F and Fc calculate the same thing, why are they written differently because Fc doesnt seem to have magnetic permeability.

Explanation / Answer

F = BIL
B = muI/2*pi*a
hence
F = mu*I^2*L/2*pi*a ( lorentz force)

now, Fc = 2I^2L*10^-6/(s + d)
Fc = 2I^2*L*10^-6/a
we know that
mu = 4*pi*10^-7
hence
Fc = 10*2*I^2*L*mu/4*pi*a
Fc = mu*I^2*L*10/2*pi*a

hence instead of 10^-6, if ther is 10^-7 in the equaiton then Fc = F ( as mu = 4*pi*10^-7)

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