Question

Magnetic filed at point ${}^{\prime }{P}^{\prime }$ due to both infinite long current carrying wires is :-

• A. $\frac{{\mu }_0}{2\pi }\otimes$
• B. $\frac{5{\mu }_0}{6\pi }\otimes$
• C. $\frac{5{\mu }_0}{6\pi }\odot$
• D. $\frac{{\mu }_0}{2\pi }\odot$

Answer 1

The correct option is B $\frac{5{\mu }_0}{6\pi }\otimes$

Magnetic field due to first wire $B_1=\frac{{\mu }_o{I}_1}{2\pi d_1}$

where $d_1=5+2.5=7.5m$

$⟹B_1=\frac{{\mu }_o\times 5}{2\pi \times 7.5}=\frac{{\mu }_o}{3\pi }$ (into the plane of paper)

Magnetic field due to second wire $B_2=\frac{{\mu }_o{I}_2}{2\pi d_2}$

where $d_2=2.5m$

$⟹B_2=\frac{{\mu }_o\times 2.5}{2\pi \times 2.5}=\frac{{\mu }_o}{2\pi }$ (into the plane of paper)

$⟹$ $B_{net}=B_1+B_2=\frac{5{\mu }_o}{6\pi }$