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, det

Question

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.

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5 months 2021-08-28T08:24:37+00:00 1 Answers 10 views 0

1. Given Information:

Current in loop = I = 62 A

Magnitude of magnetic field = B = 1.20×10⁻⁴ 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*1.20×10⁻⁴

r = 0.324 m

Therefore, the radius of this circular loop is 0.324 m