Question

Two long parallel wires placed $0.08m$ apart carry currents $3A$ and $5A$ in the same direction. The distance from the conductor carrying larger current where the resultant magnetic field is zero is

• A. 0.03 m
• B. 0.05 m
• C. 0.12 m
• D. 0.2 m

Answer 1

Answer: (B)

Let $P$ be the point where magnetic field is zero. Its distance from wire $2$ is $x$.
Magnetic field at point $P$ due to wire $1{\bar{B}}_1=\frac{{\mu }_0(3)}{2\pi (0.08-x)}\otimes$
Magnetic field at point $P$ due to wire 2 $1{\bar{B}}_2=\frac{{\mu }_0(5)}{2\pi x}\odot$
Here, ${\vec{B}}_P={\vec{B}}_1+{\vec{B}}_2=0$
or , $|{\vec{B}}_1|=|{\vec{B}}_2|$
$\frac{{\mu }_0(3)}{2\pi (0.08-x)}|=\frac{{\mu }_0(5)}{2\pi x}$
or $3x=5(0.08-x)$
or $8x=0.4$
or $x=0.05m$