A long, straight wire lies along the y-axis and carries a current I = 8.80 A in

Question

A long, straight wire lies along the y-axis and carries a current I = 8.80 A in the -y-direction (see the following figure). In addition to the magnetic field due to the current in the wire, a uniform magnetic field Be with magnitude 1.10 x 10^-6 T Is in the +x-direction. What is the total field (magnitude and direction) at the following points In the xz-plane. (Give the smallest such angles.) (a) x = 0, z = 2.00m magnitude direction from an axis parallel to the +x-direction in the xz plane (b) x = 2.00 m, z = 0 magnitude direction from an axis parallel to the +x-direction in the xz plane (c) x = 0, z = -0.50 m magnitude direction from an axis parallel to the +x-direction in the xz plane

Explanation / Answer

A) B1 = mu_o*i/(2*pi*r) = 2*10^-7*8.8/(2) = 0.88*10^-6 T

magintude is (1.1-0.88)*10^-6 = 0.22*10^-6 T

direction 0 degrees with +X-axis

B) Bnet = Sqrt(1.1^2+0.88^2)*10^-6 = 1.408 *10^-6 T

direction is theta = atan(0.88/1.1) = 38.65 degrees with X-axis

C) B1 = 2*10^-7*8.8/(0.5) = 3.52 uT

B2 = 1.1 uT

Bnet = 3.52+1.1 = 4.62*10^-6 T

0 degrees with +X-axis

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