Question

Two straight long conductors AOB and COD are perpendicular to each other and carry currents $i_1$ and $i_2$. The magnitude of the magnetic induction at a point P at a distance a from the point O in a direction perpendicular to the plane ABCD is?

• A. $\frac{{\mu }_0}{2\pi a}(i_1+i_2)$
• B. $\frac{{\mu }_0}{2\pi a}(i_1-i_2)$
• C. $\frac{{\mu }_0}{2\pi a}(i_1^2+i_2^2{)}^{1/2}$
• D. $\frac{{\mu }_0}{2\pi a}\frac{i_1{i}_2}{(i_1+i_2)}$

Answer 1

The correct option is C $\frac{{\mu }_0}{2\pi a}(i_1^2+i_2^2{)}^{1/2}$

Conductors AOB and COD are perpendicular to each other shown in figure.
At distance a above O,
$B_1=\frac{{\mu }_0{i}_1}{2\pi a}$ and $B_2=\frac{{\mu }_0{i}_2}{2\pi a}$
$B_1$ is perpendicular to $B_2$.
Resultant of $B_1$ and $B_2$
$B=\sqrt{B_1^2+B_2^2}$
$=\frac{{\mu }_0}{2\pi a}\sqrt{i_1^2+i_2^2}$.