Directions: Questions 69 and 70 are based on the following paragraph. A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. A…

Question

Directions: Questions 69 and 70 are based on the following paragraph.
A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is 30°. Another straight thin wire with steady current I₁ flowing out of the plane of the paper is kept at the origin.
The magnitude of the magnetic field (B) due to loop ABCD at the origin (O) is

Accepted Answer

(2) (μ₀ I(b-a))/(24ab). AB and CD lie along lines through O, so they give no field at O. Arc of radius r subtending θ: B=(μ₀ Iθ)/(4π r), with θ=π/6. The arcs carry current in opposite senses: B=(μ₀ I)/(4π)·π/6(1/a-1/b)=(μ₀ I(b-a))/(24ab)

Step-by-step solution

Why the other options are wrong