Question

A single loop of wire of radius 3 cm carries a current of 2.7 A. What is the magnitude of B on the axis of the loop at the following positions?

1)

the center of the loop
T

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2)

1 cm from the center
T

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3)

2 cm from the center
T

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4)

38 cm from the center

Answer 1

We know that the magnetic field B at a location x from the axisis:
               B = (μ₀ I r² ) /(2(x²+r²)^3/2)
where r = radius of the loop = 3 cm = 0.03 m
           x = the distance from the center of the loop = 0 cm , 1 cm, 2cm and 38 cm
           I = 2.7 A
       
(a) At the center of the loop , when x = 0 cm, we have
         B = 4π x10^-7 * 2.7 / 2 * 0.03
            = 5.65 x 10^-5 T

Similarly
(b) B = 4π x 10^-7 * 2.7 * 0.03*0.03 / (2(0.01*0.01 + 0.03*0.03)^3/2)
          = 4.83 x10^-5 T

(c) B = 4π x 10^-7 * 2.7 * 0.03*0.03 / (2(0.02*0.02 + 0.03*0.03)^3/2)
          = 3.26 x10^-5 T

(d) B = 4π x 10^-7 * 2.7 * 0.03*0.03 / (2(0.38*0.38 + 0.03*0.03)^3/2)
         = 2.76 x10^-8 T