Question

A wire $A$, bent in the shape of an arc of a circle, carrying a current of $2 A$ and having radius $2 cm$ and another wire $B$, also bent in the shape of arc of a circle, carrying a current of $3 A$ and having radius of $4 cm ,$ 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 }=2 cm $,
$ \theta_{ A }=2 \pi-\frac{\pi}{2}=\frac{3 \pi}{2}$
$i _{ B }=3, r _{ B }=4 cm $,
$ \theta_{ B }=2 \pi-\frac{\pi}{3}=\frac{5 \pi}{3}$
$B =\frac{\mu_{0} I \theta}{4 \pi R }$
$\frac{ B _{ A }}{ B _{ B }}=\frac{ I _{ A }}{ I _{ B }} \times \frac{\theta_{ A } R _{ B }}{\theta_{ B } R _{ A }}=\frac{6}{5}$