Question 287: Magnetism and Matter

Question

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 __________.

Accepted Answer

At point $$A$$
$$B_A=\frac{\mu_0 I}{2 \pi r}+\frac{\mu_0(2 I)}{2 \pi(3 r)}$$
At point $$C$$
$$\begin{aligned}
& B_C=\frac{\mu_0 I}{2 \pi(3 r)}+\frac{\mu_0(2 I)}{r} \
& \Rightarrow \frac{B_A}{B_C}=\frac{5}{7}
\end{aligned}$$

Magnetism and Matter

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 __________.

Integer / Numeric Answer Type