Two parallel long current-carrying wire separated by a distance are shown in the figure. The ratio of magnetic field at A to the magnetic field produced at C is . The value of is ______.

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Solution

Q.
Two parallel long current-carrying wire separated by a distance $2 r$ 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 ______. [2024]

Ans.
(5)

$B_{A} = \frac{μ_{0} I}{2 π r} + \frac{μ_{0} (2 I)}{2 π (3 r)} = \frac{5 μ_{0} I}{6 π r}$

$B_{C} = \frac{μ_{0} (2 I)}{2 π r} + \frac{μ_{0} I}{2 π (3 r)} = \frac{7 μ_{0} I}{6 π r}$

$∴$ $\frac{B_{A}}{B_{C}} = \frac{5}{7} \Rightarrow x = 5$

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