Question

create a formula giving the strength of the induced field (B) i terms of current (I) and the distance from the wire to the probe (d)

Answer 1

So we need to find the formula for magnetic field B using the current (I) and the distance from the probe (d). So, We know that the stronger the current I, the stronger the magnetic field B. That tells us that the I and B are proportional. Also we know that the strength of the magnetic field B is weaker as the distance d of the probe increases. That tells us that B and d are inversely proportional. So our formula should have B=(I/d)*c where c is a constant of proportionality. c=μ₀/2π where μ₀ is the permeability of free space. So finally our formula is B=(μ₀I)/(2πd).