Question

Two long parallel conductors are placed at right angles to a metre scale at the $2cm$ and $4cm$ marks, as shown in the figure. They carry currents of $1A$ and $3A$ respectively. They will produce zero magnetic field at the

(ignore the Earth's magnetic field)

• A. $0.5cm$ mark
• B. $2.5cm$ mark
• C. $1cm$ mark
• D. $8cm$ mark

Answer 1

Answer: (B)

$2.5cm$ mark

$|B{|}_{net}=0$

$\left(\frac{{\mu }_0{i}_1}{2\pi r_1}\right)-\left(\frac{{\mu }_0{i}_2}{2\pi r_2}\right)=0$

where $r1$ and $r_2$ are distances from wires respectively. Assuming the distance from wire 1 is $x$, then distance from wire 2 will be $2-x$

$\frac{i_1}{x}=\frac{i_2}{2-x}$

$\frac{1}{x}=\frac{3}{2-x}$

$4x=2$
$x=0.5cm$ from $1A$ wire.
distance from the y-axis $2+0.5=2.5cm$ .