Two infinitely long

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Two infinitely long, straight, parallel wires XX and YY are separated by a distance dd. They carry currents IXI_X and IYI_Y respectively in the same direction. (i) Derive an expression for the distance xx from wire XX (measured along the line joining the wires) at which the net magnetic field is zero. (ii) Using the expression obtained in part (i), calculate xx when d=8.0 cmd = 8.0\,\text{cm}, IX=20 AI_X = 20\,\text{A} and IY=50 AI_Y = 50\,\text{A}. Take μ0=4π×10−7 T m A−1\mu_0 = 4\pi \times 10^{-7}\,\text{T\,m\,A}^{-1}. (iii) Is the point where the magnetic field is zero located nearer to the wire carrying the larger current or the smaller current? Give a brief qualitative reason for your answer.

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