3. Consider two long straight wires separated by a distance of 2 m as in the Sgu

Question

3. Consider two long straight wires separated by a distance of 2 m as in the Sgure. The wires carry currents of 5A in the same direction as shown in the figure. SA Br (a) (25 points) Find the net magnetic field (magnitude and direction) at point A. Show the direction of the magnetic field of both wires and the total magnetic field in the diagram (b) (10 points) Relative to the wire 1, locate a point on the dashed line in the figure where the total magnetic field is zero. (Hint: the point is located between the two wires)

Explanation / Answer

(A) B1 = u0 I1 / 2pi (2 + 3) along -z axis

B1 = (4pi x 10^-7)(5) / (2 pi 5)

B1 = 2 x 10^-7 T

B2 = u0 I2 / 2 pi 3 = (4 pix 10^-7)(5) / (2 pi 3)

B2 = 3.33 x 10^-7 T along -z axis

B = B1 + B2 = 5.33 x 10^-7 T along -z axis

(B) this point will be inbetween the wire,

B1 = u0 I1 / (2 pi d) along -z axis

B2 = u0 I2 / (2 pi (2 - d)) along +z axis

so B1 = B2 such that B1 + B2 = 0

I1 / d = I2 / (2 - d)

2 -d = d

d = 1 m

so that is the midpoint in between the wires.

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