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Q.

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.

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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)

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a

8/3 A along positive x-axis

b

4/3 A along negative x-axis

c

5/3 A along negative x-axis

d

7/3 A along positive x-axis

answer is A.

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Detailed Solution

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×μoi2π1+14+116+⋯ ⇒  B=4μol3π=2μol3π (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 μoI2π×2=2μoi3π  Thus, I=83 A along +x-axis. 

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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)