Question

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!

a) Find the loop radius.

Express your answer with the appropriate units.

b) Find the current in the loop.

Express your answer with the appropriate units.

Answer 1

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

B_z = 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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