Question 27

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 _____

Correct Answer: 5

$$B_A = \frac{\mu_0 I}{2\pi r} + \frac{\mu_0 (2I)}{2\pi (3r)} = \frac{\mu_0 I}{2\pi r} \left(1 + \frac{2}{3}\right) = \frac{5\mu_0 I}{6\pi r}$$

$$B_C = \frac{\mu_0 I}{2\pi (3r)} + \frac{\mu_0 (2I)}{2\pi r} = \frac{\mu_0 I}{2\pi r} \left(\frac{1}{3} + 2\right) = \frac{7\mu_0 I}{6\pi r}$$

$$\frac{B_A}{B_C} = \frac{5}{7} \implies x = 5$$

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