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  4. Three long, straight and parallel wires carrying currents are arranged as shown in the figure. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/9d4de496e6e83f7f967d3f2aca7953a7-.png /> The wire C which carries a current of 50 A is so replaced that it experiences no force. The distance of wire C from wire A is

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Q. Three long, straight and parallel wires carrying currents are arranged as shown in the figure.
image
The wire $C$ which carries a current of $50\, A$ is so replaced that it experiences no force. The distance of wire $C$ from wire $A$ is

Moving Charges and Magnetism

Solution:

image
$\frac{F_{A C}}{l}=\frac{F_{B C}}{l}$
$\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \times 15 \times 50}{x}$
$=\frac{\mu_{0}}{4 \pi} \times \frac{2 \times 50 \times 10}{15-x}$
$\frac{15}{x}=\frac{10}{(15-x)}$
$225-15 x=10 x $
$\Rightarrow 25 x=255$
or $x=9\, cm$