An infinite number of straight wires each carrying current I are equally placed as shown in the figure. Adjacent wires have current in the opposite direction. The net magnetic field at point P is

Question

An infinite number of straight wires each carrying current I are equally placed as shown in the figure. Adjacent wires have current in the opposite direction. The net magnetic field at point P is, μ 0 I 4 π l ⁡ n 2 3 a k ^, μ 0 I 4 π ln 4 3 a k ^, μ 0 I 4 π ln 4 3 a - k ^, Zero

MARKS App · Accepted Answer

B 1 = μ 0 4 π I a sin α + sin β = μ 0 4 π I × 2 sin 3 0 ∘ a cos 3 0 ∘ B → = B → = B 1 k ^ + B 2 k ^ + B 3 k ^ - B 4 k ^ + ..... = μ 0 4 π I × 2 sin 3 0 ∘ a cos 3 0 ∘ k ^ - μ 0 4 π I × 2 sin 3 0 ∘ 2 a cos 3 0 ∘ k ^ + μ 0 4 π I × 2 sin 3 0 ∘ 3 a cos 3 0 ∘ k ^ + ..... = μ 0 4 π 2 I 3 a k ^ - μ 0 4 π 2 I 3 × 2 a k ^ + μ 0 4 π 2 I 3 × 3 a k ^ + ..... = μ 0 4 π 2 I 3 a 1 - 1 2 + 1 3 - 1 4 + ... k ^ = μ 0 2 I 4 π 3 a log e 1 + 1 k ^ = μ 0 2 I 4 π 3 a log e 2 k ^ = μ 0 I 4 π 3 a log e 4 k ^

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