Question

Two long straight conductors $AOB$ and $COD$ are perpendicular to each other and carry currents $I_1$ and $I_2$. The magnitude of the magnetic field 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. $\frac{{\mu }_0}{2\pi a}(i_1^2+i_2^2{)}^{.5}$
• D. $\frac{{\mu }_0}{2\pi a}\left(\frac{i_1+i_2}{i_1+i_2}\right)$

Answer 1

The correct option is C $\frac{{\mu }_0}{2\pi a}(i_1^2+i_2^2{)}^{.5}$

At the point $P$

$B_{net}=\sqrt{B_1^2+B_2^2}$

$=\sqrt{{\left(\frac{{\mu }_0}{4\pi }\frac{2i_1}{a}\right)}^2+{\left(\frac{{\mu }_0}{4\pi }\frac{2i_2}{a}\right)}^2}$

$=\frac{{\mu }_0}{2\pi a}\sqrt{i_1^2+i_2^2}$