The figure shows a wire segment of length As-4.5 cm,centered at the origin, carr

Question

The figure shows a wire segment of length As-4.5 cm,centered at the origin, carrying current2.0 A in the positive y direction (as part of some complete circuilt). To caloulate the magnitude of the magnetic field B produced by the segment at a point several meters from the origin, we can use the Biot-Savart law as ( As (ain V2. This is because r and 9 are essentially contant over the segment. Calculate B(in uni-vector notation) at the (x, y, z) coordinates (a) (o,0, 7.1 m), (b) (0, 8.4 m, 0), (e) (9.7 m, 7.3 m, 0), and (d) (-48 m 5.8m,0). (a) B (0,0,7.1 m)(Number (b) B (o, 8.4 m, o)-Number (e) B (97 m, 7.3m, o)-(Number Units Units

Explanation / Answer

a)

r = sqrt(x^2+y62+z^2) = 7.1 m

B = (4*pi*10^-7*2*4.5*10^-2)/(4*pi*7.1^2) = 1.78*10^-10 T i

(b)

r = 8.4 m

B = (4*pi*10^-7*2*4.5*10^-2*sin0)/(4*pi*8.4^2) = 0

(c)

r = sqrt(9.7^2+7.3^2+0) = 12.14 m

B = (4*pi*10^-7*2*4.5*10^-2*sin90)/(4*pi*12.14^2)

B = 5.46*10^-11 T -k

(d)

r = sqrt(4.8^2+5.8^2+0) = 7.53 m

B = (4*pi*10^-7*2*4.5*10^-2*sin90)/(4*pi*7.53^2)

B = 1.42*10^-10 T k

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