Infinite wires, each carrying a current $$0.5$$ A, are kept parallel to $$y-axis$$ and intersecting $$x-axis$$ at x $$=$$ ±$$1$$ m, ±$$2$$ m, ±$$4$$ m, ±$$8$$ m, etc. Wires kept at positive values of x carry current in the same direction while wires kept at negative values of x carry current successively in opposite directions as shown in figure.A wire is kept parallel to $$x-axis$$ and intersecting $$y-axis$$ at $$2$$ m. It carries a current i. Assuming this wire to be insulated from others then the current i in it such that magnetic induction at O is zero is:(Assume$$ each wire to be infinitely $$long)

Question

Infinite wires, each carrying a current $$0.5$$ A, are kept parallel to $$y-axis$$ and intersecting $$x-axis$$ at x $$=$$ ±$$1$$ m, ±$$2$$ m, ±$$4$$ m, ±$$8$$ m, etc. Wires kept at positive values of x carry current in the same direction while wires kept at negative values of x carry current successively in opposite directions as shown in figure.A wire is kept parallel to $$x-axis$$ and intersecting $$y-axis$$ at $$2$$ m. It carries a current i. Assuming this wire to be insulated from others then the current i in it such that magnetic induction at O is zero is:(Assume$$ each wire to be infinitely $$long)

Infinity Learn · Accepted Answer

Given that wires kept at negative x values carry current successively in opposite directions. The fields due to wires kept at $$x=$$±$$2$$ m,±$$8$$ m  etc. cancel each other. Due to wires kept at $$x=$$±$$1$$ m,±$$4$$ m, fields are in upward direction and net field is given by: $$B=2$$×μ$$oi2$$$$π$$$$1+14+116+$$⋯ ⇒  $$B=4$$μ$$ol3$$π$$=2$$μ$$ol3$$π $$(Since$$ $$i=0.5$$ A This field is negated by field due to wire placed at y $$-$$ $$2$$ m. This wire must carry current l along positive $$x-axis$$ such that μ$$oI2$$π×$$2=2$$μ$$oi3$$π  Thus, $$I=83$$ A along $$+x-axis$$.

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