Two very long conducting parallel wires are separated by a distance d from each other and equal currents are passed through them in mutually opposite directions. A particle of charge q passes through a point, at a distance /d2 from both wires, with velocity v perpendicularly to the plane formed by…

Question

Two very long conducting parallel wires are separated by a distance d from each other and equal currents are passed through them in mutually opposite directions. A particle of charge q passes through a point, at a distance /d2 from both wires, with velocity v perpendicularly to the plane formed by the wires. The resultant magnetic force acting on this particle is ......

Accepted Answer

(4) 0. Given: two long parallel wires a distance d apart carrying equal currents in opposite directions; a charge q moves with speed v through the midpoint, perpendicular to the plane containing the wires. Idea: find the field at that point first, then the angle between it and ⃗v. Each wire is /d2 away, so each contributes (μ₀ I)/(2π(d/2))=(μ₀ I)/(π d); the currents being opposite, the two fields point the same way at the midpoint and add to (2μ₀ I)/(π d). That resultant field is perpendicular to the plane containing the two wires. The velocity is perpendicular to the same plane, so ⃗v is parallel to ⃗B and the angle between them is zero. F=qvB sin 0°=0: the magnetic force on the particle is zero.

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