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The magnetic field produced by a current I in a coil is B₁ = μ₀I/2R, and the field produced by a current 2I in the same coil is B₂ = μ₀(2I)/2R. The combined magnetic field, Bnet, is determined using the formula Bnet = √(B₁² + B₂² + 2B₁B₂ cosθ), where θ is 90°. What is the value of Bnet?

  1. Bnet = √(B₁² + B₂² + 2B₁B₂ cosθ)
  2. Bnet = √(B₁² + B₂²)
  3. Bnet = √5μ₀I/2R
  4. None of these

Correct answer: Bnet = √(B₁² + B₂²)

Solution

Since θ = 90°, cosθ = 0. Substituting this into the formula, Bnet = √(B₁² + B₂²). This matches option B.

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