Consider two parallel conducting wires along the direction of the z axis as show
ID: 1909941 • Letter: C
Question
Consider two parallel conducting wires along the direction of the z axis as shown below. Wire 1 crosses the x-axis at x = -2.00 cm and carries a current of 3.60 A out of the xy-plane of the page. Wire 2 (right) crosses the x axis at x = 2.00 cm and carries a current of 8.20 A into the xy plane.Explanation / Answer
Using the right-hand rule, the magnetic field from the wire at x = -1.90 cm is counter-clockwise (current upward, thumb upward, fingers curve ccw). Conversely, the magnetic field from the wire at +1.90 cm is clockwise. Between the wires, the fields are in the same direction and must add directly, so there can be no zero point in that area. The field magnitude around each wire is I*µ0/(2*p*r), where r is the distance from the wire. For |x| > 1.90: The field magnitude from wire 1 is I1*µ0/2*p*(x + 1.80) The field magnitude from wire 2 is I2*µ0/2*p*(x - 1.80) The zero point occurs when these magnitudes are equal (since they are in opposite directions) I1*µ0/2*p*(x + 1.80) = I2*µ0/2*p*(x - 1.80) I1/(x + 1.80) = I2/(x - 1.80) I1*(x - 1.80) = I2*(x + 1.80) (I1 - I2)*x = 1.80*(I1 + I2) x = 1.80*(I1 + I2)/(I1 - I2) x = -2.67 cm