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4. Moving charges and magnetism — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics4. Moving charges and magnetism1 Mark
MCQ
Two mutually perpendicular insulated conducting wires carrying equal currents $I$, intersect at origin. Then the resultant magnetic induction at point $P(2m, 3m)$ will be
  • A
    $\frac{{{\mu _0}I}}{{5a}}$
  • B
    $\frac{{5{\mu _0}I}}{{2\pi }}$
  • ✓
    $\frac{{{\mu _0}I}}{{12\pi }}$
  • D
    zero
✓

Answer

Correct option: C.
$\frac{{{\mu _0}I}}{{12\pi }}$
c
We know that, magnetic field due to an infinite wire is given by,

$B_{\text {net }}=\frac{\mu_0 I}{2 \pi(d)}$

Due to long wire along $x$ - axis,

magnetic field at $P$ is $B_x=\frac{\mu_0 I}{2 \pi(3)} \odot$

Due to long wire along $y$-axis,

magnetic field at $P$ is $B_y=\frac{\mu_0 I}{2 \pi(2)} \otimes$

Net magnetic field at $P$ is $B_{\text {net }}=B_y-B_x$

$B_{\text {net }}=\frac{\mu_0 I}{2 \pi(2)}-\frac{\mu_0 l}{2 \pi(3)}$

$\Rightarrow B_{\text {net }}=\frac{\mu_0 I}{12 \pi} \otimes$

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