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Two infinitely long thin wires are placed at $(1 \mathrm{~cm}, 0 \mathrm{~cm})$ and $(2 \mathrm{~cm}, 0 \mathrm{~cm})$ as shown in the figure.
The same current $i$ flows in both the wires in the same direction, say, into the page. Let the magnetic field at the origin due to these wires is $\overrightarrow{\mathrm{B}}$. If $\mathrm{B}_0$ is the magnitude of the magnetic field if only the wire at $(1 \mathrm{~cm}, 0 \mathrm{~cm})$ was present, then the value of $\mathrm{B} / \mathrm{B}_0$ is
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The same current $i$ flows in both the wires in the same direction, say, into the page. Let the magnetic field at the origin due to these wires is $\overrightarrow{\mathrm{B}}$. If $\mathrm{B}_0$ is the magnitude of the magnetic field if only the wire at $(1 \mathrm{~cm}, 0 \mathrm{~cm})$ was present, then the value of $\mathrm{B} / \mathrm{B}_0$ is
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Verified Answer
The correct answer is:
$3 / 2$
$\overline{\mathrm{B}}=\frac{\mu_0 \mathrm{i}}{2 \pi}\left[\frac{1}{10^{-2}}+\frac{1}{2 \times 10^{-2}}\right] \hat{\mathrm{j}}$
$$
=2 \times 10^{-7} \times \mathrm{i} \times 150 \hat{\mathrm{j}}
$$
and, $\overrightarrow{\mathrm{B}}_0=\frac{\mu_0 \mathrm{i}}{2 \pi} \times \frac{1}{10^{-2}}=2 \times 10^{-7} \times \mathrm{i} \times 100 \hat{\mathrm{j}}$
So, $\frac{\mathrm{B}}{\mathrm{B}_0}=\frac{3}{2}$
$$
=2 \times 10^{-7} \times \mathrm{i} \times 150 \hat{\mathrm{j}}
$$
and, $\overrightarrow{\mathrm{B}}_0=\frac{\mu_0 \mathrm{i}}{2 \pi} \times \frac{1}{10^{-2}}=2 \times 10^{-7} \times \mathrm{i} \times 100 \hat{\mathrm{j}}$
So, $\frac{\mathrm{B}}{\mathrm{B}_0}=\frac{3}{2}$
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