Eduprobe
Question:
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^o. Another straight thin wire with steady current I_1 flowing out of the plane of the paper is kept at the origin. Due to the presence of the current I_1 at the origin :
the forces on AB and DC are zero
the magnitude of the net force on the loop is given by μ₀ I I₁/24ab(b-a)
the forces on AD and BC are zero
the magnitude of the net force on the loop is given by I₁ I/4πμ₀ [2(b-a)+π/3(a+b)]
Solution:
The forces on AD and BC are zero because magnetic field due to a straight wire on AD and BC is parallel to elementary length of the loop⇒ F = I(l⃗×B⃗) = 0