Let two long parallel wires a distance ‘d’ apart, carry equal current ‘i’ in the same direction. One wire is at $$x=0$$, the other at $$x=d$$. Determine magnetic field at any point on $$x-axis$$ between the wires as a function of ‘x’.

Question

Let two long parallel wires a distance  ‘d’ apart, carry equal current ‘i’ in the same direction. One wire is at  $$x=0$$, the other at  $$x=d$$. Determine magnetic field at any point on $$x-axis$$ between the wires as a function of  ‘x’.

Infinity Learn · Accepted Answer

Let us consider a point ‘P’ at a distance (x$$,$$y) from the wire $$1$$.   $$0$$≤x≤dHence  B→$$1=$$μ$$0i2$$$$π$$$$xj^The$$ point is at a distance d−x from wire $$2$$. ∴ B→$$2=$$−μ$$0i2$$π$$(d$$−$$x)j^$$ ∴ B→$$net=B$$→$$1+B$$→$$2=$$μ$$0i2$$$$π$$$$xj^$$−μ$$0i2$$π$$(d$$−$$x)j^B$$→$$net=$$μ$$0i(d$$−$$2x)2$$$$π$$$$x(d$$−$$x)j^$$ .

Let two long parallel wires a distance ‘d’ apart, carry equal current ‘i’ in the same direction. One wire is at x=0, the other at x=d. Determine magnetic field at any point on x-axis between the wires as a function of ‘x’.

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