Question

Two straight long conductors $\text{AOB}$ and $\text{COD}$ are perpendicular to each other and carries currents $i_1$ and $i_2$ respectively. The magnitude of magnetic induction at a point $\text{P}$ at a distance $a$ from the point $\text{O}$ in a direction perpendicular to the plane $\text{ACBD}$ is

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

Answer 1

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

Field due to a long straight conductor is,

$B=\frac{{\mu }_{0}i}{2\pi r}$



Due to the given conductors $\text{AOB}$ and $\text{COD}$ net field at point $\text{P}$ is,

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

$=\sqrt{{\left(\frac{{\mu }_0{i}_1}{2\pi a}\right)}^2+{\left(\frac{{\mu }_0{i}_2}{2\pi a}\right)}^2}$

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

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.