Eduprobe
Question:
A current I is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is μ₀IR (MA=R, MB=2R, ∠DMA=90°).
5/16, but out of the plane of the paper
7/16, but out of the plane of the paper
7/16, but into the plane of the paper
5/16, but into the plane of the paper
Solution:
Magnetic field at the centre M due to current through the curved portion DA is →B₁ = μ₀I/4πR × (3π/2) = 3μ₀I/8R ⦩
Magnetic field at the centre M due to current through the straight portion AB is B₂ = 0, since point M lies on the axis of the straight portion AB.
Magnetic field at the centre M due to current through the curved portion BC is →B₃ = μ₀I/4π2R × π/2 = μ₀I/16R ⦩
Magnetic field at the centre M due to current through the straight portion CD is B₄ = 0, since point M lies on the axis of the straight portion CD.
The resultant magnetic field at the point M is →B = →B₁ + →B₂ + →B₃ + →B₄ = (3μ₀I/8R + 0 + μ₀I/16R + 0) ⦩ = 7μ₀I/16R ⦩.