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NTA Abhyas JEE Main2020PhysicsMagnetic Effects of CurrentPractice

Two identical wires A and B , each of length ' l ', carry the same current I . Wire A is bent into a circle of radius R and wire B is bent to form a square of side ' a '. If B A and B B are the values of magnetic field at the centres of the circle and square respectively, then the ratio B A B B is

Options

  1. Aπ 2 16
  2. Bπ 2 8 2
  3. Cπ 2 8
  4. Dπ 2 16 2

Correct answer

B. π 2 8 2

Step-by-step solution

2 π R = 4 a a R = 2 π 4 ⇒ a R = π 2 B A = μ 0 i 2 R B B = μ 0 i π a 2 2 B A B B = μ 0 i 2 R × π a 2 2 μ 0 i = π a 4 2 R = π 4 2 π 2 = π 2 8 2

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