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Two concentric circular coils P and Q have radii 16 cm and 10 cm respectively, and both lie in the same vertical plane along the north-south direction. Coil P has 20 turns carrying 16 A; coil Q has 25 turns carrying 18 A. When viewed by an observer facing west, the current in P is anticlockwise and in Q is clockwise. Find the magnitude and direction of the net magnetic field at the common centre of the coils.
- 1.6 * 10⁻³ T directed towards west
- 1.6 * 10⁻³ T directed towards east
- 1.6 * 10⁻⁵ T directed towards east
- 1.6 * 10⁻⁵ T directed towards west
Correct answer: 1.6 * 10⁻³ T directed towards east
Solution
B_P = mu₀ * N_P * I_P / (2 * R_P) = (4 * pi * 10⁻⁷ * 20 * 16) / (2 * 0.16) = 4 * pi * 10⁻⁴ T (towards west). B_Q = mu₀ * N_Q * I_Q / (2 * R_Q) = (4 * pi * 10⁻⁷ * 25 * 18) / (2 * 0.10) = 9 * pi * 10⁻⁴ T (towards east). Net B = (9 - 4) * pi * 10⁻⁴ = 5 * pi * 10⁻⁴ T = 1.57 * 10⁻³ T ≈ 1.6 * 10⁻³ T, directed towards east.
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