A 2.0 meter length of straight conducting wire carries a current of 10.0 A. a) F

Question

A 2.0 meter length of straight conducting wire carries a current of 10.0 A. a) Find the resulting magnetic field at a distance of 10.0 cm from the wire. b) If this wire is now wrapped to form a circular coif with a 10.0 cm radius, find the value of the resulting magnetic field at the center of the coif. (Note that you will need to compute the number of loops N that can be made from a 2.0m length of wire.) c) Compare the strength of the magnetic field for parts a and b and compute their ratio B_b/B_a. In other words, how many limes stronger is the field for the coif?

Explanation / Answer

(A) B = u0 I / (2 pi r)

= (4pi x 10^-7)(10) / (2 x pi x 0.10)

= 2 x 10^-5 T

(B) N( 2 pi r) = L

N = 2 / (2 x pi x 0.10) = 3.183 tunrs.

B = u0 N I / 2 R

= (4pi x 10^-7 x 3.183 x 10 ) / (2 x 0.10)

= 2 x 10^-4 T

(C) Bb/ Ba = 2 / 0.2 = 10 times

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