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 23.0 cm from the loop center.
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.
Homework Answers
A) at the centre of loop,
B =u0 * I / 2r
41.2 x 10^-6 = (4pi x 10^-7 x I) / (2r)
I/r = 65.57
I = 65.57r
B = (u0 * I* r^2 ) / (2 * (x^2 + r^2)^(3/2)) .....magnetic field on
axis .
5.15 x 10^-9 = [4pi x 10^-7 x 65.57r x r^2 ] / [ 2 ( 0.23^2 + r^2 )^3/2 ]
10.3 x 10^-9 ( 0.23^2 + r^2 )^3/2 = 8.24 x 10^-5 x r^3
( 0.23^2 + r^2 )^3/2 / (r ^3 ) = 7999.78
(0.0529 + r^2 )^(1/2) = 20r
0.0529 + r^2 = 400r^2
r = 0.0115 m Or 1.15 cm .......Ans
B) I = 65.57 x 0.0115 = 0.755 A ......Ans
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