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Moving Charges and Magnetism — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMoving Charges and Magnetism3 Marks
Question
The figure shows three infinitely long straight parallel current carrying conductors. Find the
  1. magnitude and direction of the net magnetic field at point A lying on conductor 1,
  2. magnetic force on conductor 2.
✓

Answer

  1. $B_2=\frac{\mu_0}{4\pi}\frac{2(3I)}{r}=\frac{\mu_0}{4\pi}\big(\frac{6I}{r}\big)$into the plane of the paper/$(\otimes)$.
$B_3=\frac{\mu_0}{4\pi}\frac{2(4I)}{3r}=\frac{\mu_0}{4\pi}\big(\frac{8I}{3r}\big)$out of the plane of the paper/$(\bigodot)$.

$B_A=B_2-B_3$ into the paper.

$=\frac{\mu_0}{4\pi}\Big(\frac{10I}{3r}\Big) into\text{ }the\text{ }paper.\text{} (\otimes)$
  1. $F_{21}=\frac{\mu_0}{4\pi}\frac{2I(3I)}{r}$ away from wire1 (/towards 3)
$F_{23}=\frac{\mu_0}{4\pi}\frac{2(3I)(4I)}{2r}$ away from wire 3 (towards 1)

$F_{\text{net}}=F_{23}-F_{21}$ towards wire1

$=\frac{\mu_0}{4\pi}\frac{6(I)^2}{r}$ towards wire1

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