Two long parallel wires carrying currents 8 ,A and 15 ,A in oppos… - Vidyadip

MCQ

Two long parallel wires carrying currents $8\,A$ and $15\,A$ in opposite directions are placed at a distance of $7\,cm$ from each other. A point $P$ is at equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnitude of magnetic field at $P$ is $............\times 10^{-6}\,T$. (Given : $\left.\sqrt{2}=1.4\right)$

A
$65$
✓
$68$
C
$66$
D
$67$

✓

Answer

Correct option: B.

$68$

b
Magnetic fields due to both wires will be perpendicular to each other.

$B _1=\frac{\mu_0 i _1}{2 \pi d } \quad B _2=\frac{\mu_0 i _2}{2 \pi d }$

$B _{\text {net }}=\sqrt{ B _1^2+ B _2^2} \Rightarrow \frac{\mu_0}{2 \pi d } \sqrt{ i _1^2+ i _2^2}$

$\Rightarrow \frac{4 \pi \times 10^{-7}}{2 \pi \times(7 / \sqrt{2}) \times 10^{-2}} \times \sqrt{8^2+15^2}\left( d =\frac{7}{\sqrt{2}}\,cm \right)$

$\Rightarrow 68 \times 10^{-6}\,T$

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