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 isflowing 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 :

• A. the forces on AB and DC are zero
• B. the forces on AD and BC are zero
• C. the magnitude of the net force on the loop is given by $\frac{I_{1}I}{4\pi }{\mu }_0\left[2\right(b-a)+\frac{\pi }{3}(a+b\left)\right]$
• D. the magnitude of the net force on the loop is given by $\frac{{\mu }_{0}I{I}_1}{24ab}(b-a)$

Answer 1

Answer: (B)

the forces on AD and BC are zero

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
$\overrightarrow{F}=I(\overrightarrow{\ell }\times \overrightarrow{B})=0$