Question
Two parallel long current carrying wire separated by a distance $2r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$ The value of $x$ is $........$
✓
Answer
$ B _{ A }=\frac{\mu_0 i }{2 \pi r }+\frac{\mu_0(2 i )}{2 \pi(3 r )}=\frac{5 \mu_0 i }{6 \pi r }$
$B _{ C }=\frac{\mu_0(2 i )}{2 \pi r }+\frac{\mu_0 i }{2 \pi(3 r )}=\frac{7 \mu_0 i }{6 \pi r }$
$\therefore \frac{ B _A}{B_{ C }}=\frac{5}{7}$
$\therefore x =5$
$B _{ C }=\frac{\mu_0(2 i )}{2 \pi r }+\frac{\mu_0 i }{2 \pi(3 r )}=\frac{7 \mu_0 i }{6 \pi r }$
$\therefore \frac{ B _A}{B_{ C }}=\frac{5}{7}$
$\therefore x =5$
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