If a single circular loop of wire carries a current of 62 A and produces a magnetic field at its center with a magnitude of 1.20 10-4 T, determine the radius of the loop.

Given Information:  

Current in loop = I = 62 A

Magnitude of magnetic field = B = 1.20x10⁻⁴ T

Required Information:  

Radius of the circular loop = r = ?  

Radius of the circular loop = 0.324 m

Explanation:  

In a circular loop of wire with radius r and carrying a current I  induces a magnetic field B which is given by

B = μ₀I/2r

Please note that for an infinitely straight long wire we use 2πr whereas for circular loop we use 2r

Where μ₀= 4πx10⁻⁷ is the permeability of free space

Re-arranging the equation yields

r = μ₀I/2B

r = 4πx10⁻⁷*62/2*1.20x10⁻⁴

r = 0.324 m

Therefore, the radius of this circular loop is 0.324 m

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