Question

A wire $A$, bent in the shape of an arc of a circle, carrying a current of $2A$ and having radius $2cm$ and another wire $B$, also bent in the shape of arc of a circle, carrying a current of $3A$ and having radius of $4cm,$ are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is:

• A. 4 : 6
• B. 6 : 4
• C. 6 :5
• D. 2 : 5

Answer 1

Answer: (C)

Given $i_A=2,r_A=2cm$,
${\theta }_A=2\pi -\frac{\pi }{2}=\frac{3\pi }{2}$
$i_B=3,r_B=4cm$,
${\theta }_B=2\pi -\frac{\pi }{3}=\frac{5\pi }{3}$
$B=\frac{{\mu }_{0}I\theta }{4\pi R}$
$\frac{B_A}{B_B}=\frac{I_A}{I_B}\times \frac{{\theta }_A{R}_B}{{\theta }_B{R}_A}=\frac{6}{5}$