Question

There wires are situated at the same distance. A current of $1A$, $2A$, $3A$ flows through these wires in the same direction. What is ratio $F_1/F_2$ where $F_1$ is force on $1$ and $F_2$ on $2$?

• A. $7/8$
• B. $1$
• C. $9/8$
• D. none of the above

Answer 1

Answer: (A)

$7/8$

Force per unit length is given as $F=\frac{{\mu }_{\circ }\times I_1\times I_2}{2\pi d}$

Force on wire 1 due to wires 2 and 3 is given as

$F_1=I_1\times (\frac{{\mu }_{\circ }{I}_2}{2\pi d}$ $+\frac{{\mu }_{\circ }{I}_3}{2\pi 2d})$

Given $I_1=1A,I_2=2A$, $I_3=3A$

$F_1=\frac{{\mu }_{\circ }2}{2\pi d}$ $+\frac{{\mu }_{\circ }3}{4\pi d}$

$F_1=\frac{7{\mu }_{\circ }}{4\pi d}$

$I_1=1A$, $I_3=3A$

Force on wire 2 due to wires 1 and 3 is given as

$F_3=I_{2}A\times (\frac{{\mu }_{\circ }{I}_1}{2\pi d}$ $-\frac{{\mu }_{\circ }{I}_3}{2\pi d})$

$F_2=2A\times (\frac{{\mu }_{\circ }1}{2\pi d}$ $-\frac{{\mu }_{\circ }3}{2\pi d})$

$F_2=-\frac{4{\mu }_{\circ }}{2\pi d}$

$\frac{F_1}{F_2}=\frac{7}{8}$