Question

Two long parallel wires P and Q are held perpendicular to the plane of paper with distance of 5 m between them. If P and Q carry current of 2.5 amp. and 5 amp. respectively in the same direction, then the magnetic field at a point half-way between the wires is

• A. ${\mu }_0/17$
• B. $\sqrt{3}{\mu }_0/2\pi$
• C. ${\mu }_0/2\pi$
• D. $3{\mu }_0/2\pi$

Answer 1

Answer: (C)

${\mu }_0/2\pi$

Since the fileds created by $i_1$ and $i_2$ will be in opposite direction,

$B=\frac{{\mu }_0}{4\pi }\frac{2i_2}{\left(r/2\right)}-\frac{{\mu }_0}{4\mu }\frac{2i_1}{\left(r/2\right)}=\frac{{\mu }_0}{4\pi }\frac{4}{r}(i_2-i_1)$

$=\frac{{\mu }_0}{4\pi }\frac{4}{5}(5-2.5)=\frac{{\mu }_0}{2\pi }$