Each of the current-carrying wires in the figure below is long and straight and

Question

Each of the current-carrying wires in the figure below is long and straight and carries a current of I_1 = 2.0 A, I_2 = 4.0 A, and I_3 = 8.0 A either into or out of the page as shown. The wires are separated by a distance of 0.25 m. a) Identify the directions of the magnetic B_1 and B_2 due to the currents I_1 and I_2 at the fields location of wire 3. (You might use the figure above) (b) What is the direction relative to the x-axis and the magnitude of the net magnetic field at the location of wire 3 due to the currents I_1 and I_2?

Explanation / Answer

The magnetic field due to an infinitely long straight wire is given by,

B = 0I/2r

Magnetic field due to current I2 (B2) = 0(I2)/2r

=> B2 = (4*10-7)(4)/(2**0.35)

=> B2 = 22.86*10-7 T (directed in south direction)

Magnetic field due to current I1 (B1) = 0(I1)/2r

=> B1 = (4*10-7)(2)/(2**0.35)

=> B1 = 11.43*10-7 T (directed 600 in anticlockwise direction with respect to the x-axis)

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Net magnetic field in the x- direction (Bx) = B1x = B1*cos(600) = 5.7*10-7 T

Net magnetic field in the y- direction (By) = B1y - B2 = B1*sin(600) - B2 = -12.96*10-7 T

Net magnetic field (B) = (Bx2 + By2) = 14.16*10-7 T

angle = tan-1(By/Bx) = 66.250

B is directed 66.250 in the clockwise direction with respect to the x-axis

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