Question

# A single-turn wire loop produces a magnetic field of 41.2 μT at its center, and 5.15...

A single-turn wire loop produces a magnetic field of 41.2 μT at its center, and 5.15 nT on its axis, at 22.0 cm from the loop center. Hint: you can use the Biot-Savart Law to derive an expression for the field away from the center of a loop. This is done in the Wolfson textbook as an example problem, so you can use that result if you wish!

b) Find the current in the loop.

Derivation:

Magnetic Field at the center of loop :-

We know the Biot Savart law

or,

At the loop center, = 900

So,

or,

or,

Magnetic field on axis of loop:-

(a)

Given,

B = 41.2 x 10-6 T

Bz = 5.15 x 10-9 T

Z = 22.0 cm = 0.22 m

Putting these values in the above derived equationes, we get

.....................................(1)

and .....................................(2)

Dividing equation (2) by (1), we get

or,

or,

or,

or,

(a)

Putting the value of R in equation (1),

or,

or,

or,

or,

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