The figure shows three infinitely long straight parallel current … - Vidyadip

Question

The figure shows three infinitely long straight parallel current carrying conductors. Find the:

Magnitude and direction of the net magnetic field at point A lying on conductor 1.
Magnetic force on conductor 2.

✓

Answer

$B_2=\frac{\mu_0}{4\pi}\frac{2(3I)}{r}=\frac{\mu_0}{4\pi}\big(\frac{6I}{r}\big)$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.

$=\frac{\mu_0}{4\pi}\Big(\frac{10I}{3r}\Big) into\text{ }the\text{ }paper.\text{} (\otimes)$

$F_{21}=\frac{\mu_0}{4\pi}\frac{2I(3I)}{r}$ 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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