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A wire is bent in the form of a circular arc of radius r with a straight portion A B . If the current in the wire is i , then the magnetic induction at point O is

Options

  1. Aμ 0 i 2 π r tan ⁡ ϕ
  2. Bμ 0 i 2 π r π - ϕ
  3. Cμ 0 i 2 π r π - ϕ + tan ⁡ ϕ
  4. Dμ 0 i 2 π r π - tan ⁡ ϕ

Correct answer

C. μ 0 i 2 π r π - ϕ + tan ⁡ ϕ

Step-by-step solution

B = B 1 + B 2 = μ 0 i 4 π r 2 π - 2 ϕ + μ 0 i 4 π d 2 sin ⁡ ϕ Where cos ⁡ ϕ = d r d = r cos ⁡ ϕ B = μ 0 i 4 π r [ 2 π − 2 ϕ + 2 tan ϕ ] B = μ 0 i 2 π r [ π − ϕ + tan ϕ ]

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