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 axis carry current in the same direction while wires kept at negative values of x axis carry current successively in opposite directions as shown in figure. A wire is kept parallel to $$x-axis$$ and intersecting $$y-axis$$ at $$y=2m$$ . 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 axis carry current in the same direction while wires kept at negative values of  x axis carry current successively in opposite directions as shown in figure. A wire is kept parallel to  $$x-axis$$ and intersecting  $$y-axis$$ at $$y=2m$$ . 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 out of the page and net field is given by: $$B=2$$×μ$$0i2$$$$π$$$$1+14+116+$$....⇒ $$B=4$$μ$$0i3$$π$$=2$$μ$$03$$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 I along positive  $$x-axis$$ such that  μ$$0I2$$π×$$2=2$$μ$$03$$$$π$$Thus,  $$I=83A$$ along $$+$$  $$x-axis$$.$$=$$ $$0002.67$$

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