99 Percentile Qs Bank for JEE MainPhysicsMagnetic Effects of Current
A rectangular loop of metallic wire is of length a and breadth b and carries a current i . The magnetic field at the centre of the loop is
Options
- Aμ 0 i 4 π 8 a 2 + b 2 a b
- Bμ 0 i 4 π 4 a 2 + b 2 a b
- Cμ 0 i 4 π 2 a 2 + b 2 a b
- Dμ 0 i 4 π a 2 + b 2 a b
Correct answer
A. μ 0 i 4 π 8 a 2 + b 2 a b
Step-by-step solution
From figure it is clear that B A B = B C D = μ 0 i 4 π b 2 sin ϕ 1 + sin ϕ 2 = μ 0 4 π ⋅ 4 i b ⋅ a a 2 + b 2 B B C = B D A = μ 0 4 π ⋅ 4 i a ⋅ b a 2 + b 2 ∴ B = B A B + B B C + B C D + B D A B = 2 μ 0 4 π ⋅ 4 i b ⋅ a a 2 + b 2 + 2 μ 0 4 π ⋅ 4 i a ⋅ b a 2 + b 2 B = μ 0 4 π ⋅ 2 × 4 i a 2 + b 2 a b + b a B = μ 0 4 π ⋅ 8 i a 2 + b 2 a b