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Two infinitely long, thin, straight parallel wires are separated by a distance of 0.1 m and each carries a current of 10 A. A point P is equidistant from both wires at a distance of 0.1 m from each. Find the magnitude of the net magnetic field at P when the currents flow in (i) the same direction and (ii) opposite directions.
- Same direction: B = 2*sqrt(3) * 10⁻⁵ T; Opposite direction: B = 2 * 10⁻⁵ T
- Same direction: B = 2 * 10⁻⁵ T; Opposite direction: B = 2*sqrt(3) * 10⁻⁵ T
- Same direction: B = sqrt(3) * 10⁻⁵ T; Opposite direction: B = 10⁻⁵ T
- Same direction: B = 0; Opposite direction: B = 2*sqrt(3) * 10⁻⁵ T
Correct answer: Same direction: B = 2*sqrt(3) * 10⁻⁵ T; Opposite direction: B = 2 * 10⁻⁵ T
Solution
The two wires are 0.1 m apart, and P is 0.1 m from each, so the triangle is equilateral with all angles 60 deg. The magnetic field from each wire has magnitude B0 = (4*pi*10⁻⁷ * 10) / (2*pi * 0.1) = 2*10⁻⁵ T. For same-direction currents, by the right-hand rule both B vectors at P point such that the angle between them is 60 deg, giving net B = 2*B0*cos(30 deg) = 2*10⁻⁵ * sqrt(3) = 2*sqrt(3)*10⁻⁵ T. For opposite-direction currents, the angle between B1 and B2 is 120 deg, giving net B = 2*B0*cos(60 deg) = 2*10⁻⁵ * 1 = 2*10⁻⁵ T.
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