Question

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

• A. $0.5m$
• B. $0.04m$
• C. $0.05m$
• D. $0.4m$

Answer 1

Answer: (C)

$0.05m$

Let magnetic field at point P is zero.

Magnetic field at point P due to wire 1,

$B_1=\frac{{\mu }_o{I}_1}{2\pi (0.08-x)}$ into the plane of paper

Magnetic field at point P due to wire 2,

$B_2=\frac{{\mu }_o{I}_2}{2\pi \left(x\right)}$ out of the plane of paper

$\therefore$ $\frac{{\mu }_o{I}_1}{2\pi (0.08-x)}=\frac{{\mu }_o{I}_2}{2\pi x}$

Or $\frac{I_1}{0.08-x}=\frac{I_2}{x}$

$\therefore$ $\frac{3}{0.08-x}=\frac{5}{x}$

$⟹x=0.05m$