# Two straight long conductors AOB and COD are perpendicular to each other and carry currents i1 and i2. 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 ACBD is Option 1) $\frac{\mu 0\left ( i1+i2 \right )}{2\pi a}$ Option 2) $\frac{\mu 0\left ( i1-i2 \right )}{2\pi a}$ Option 3) $\frac{\mu 0\left ( (i1)^{2}+(i2)^{2} \right )^{\frac{1}{2}}}{2\pi a}$ Option 4) $\frac{\mu 0 i1 i2 }{\left ( l1+l2 \right )2\pi a}$

P Plabita

As we learnt in

For Infinite Length -

$\phi_{1}=\phi_{2}=90^{\circ}$

$B=\frac{\mu_{o}}{4\pi}\:\frac{2i}{r}\:$

- wherein

Magnetic field due to both AOB and COD are respectively :

$B_{1}= \frac{\mu_{0}i_{1}}{2 \pi a}\:\:\:\:\: and\:\:\:\:\: B_{2}=\frac{\mu_{0}i_{2}}{2 \pi a}$

$B_{1}$ and $B_{2}$ are perpendicular to each other.

$\Rightarrow B= \sqrt {B^{2}_{1}+B^{2}_{2}}= \frac{\mu_{o}}{2 \pi a} \sqrt {i^{2}_{1}+i^{2}_{2}}$

Option 1)

$\frac{\mu 0\left ( i1+i2 \right )}{2\pi a}$

This option is incorrect.

Option 2)

$\frac{\mu 0\left ( i1-i2 \right )}{2\pi a}$

This option is incorrect.

Option 3)

$\frac{\mu 0\left ( (i1)^{2}+(i2)^{2} \right )^{\frac{1}{2}}}{2\pi a}$

This option is correct.

Option 4)

$\frac{\mu 0 i1 i2 }{\left ( l1+l2 \right )2\pi a}$

This option is incorrect.

Exams
Articles
Questions