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 1

The magnetic field at point $A$, $B_A$, is given by:
$B_A = \frac{\mu_0 I}{2 \pi r} + \frac{\mu_0 (2I)}{2 \pi (3r)} = \frac{5 \mu_0 I}{6 \pi r}.$
**The magnetic field at point $C$, $B_C$, is given by: **
$B_C = \frac{\mu_0 (2I)}{2 \pi r} + \frac{\mu_0 I}{2 \pi (3r)} = \frac{7 \mu_0 I}{6 \pi r}.$
**The ratio of magnetic fields $B_A$ to $B_C$ is: **
$\frac{B_A}{B_C} = \frac{5}{7}.$
**Thus, we find: **
$x = 5.$