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}

 

Answers (1)

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.

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