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

Answer 1

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


The magnetic induction at the point P due to AOB and COD is along perpendicular directions hence the magnitude
At $P:B_{net}=\sqrt{B_1^2+B_2^2}$
$=\sqrt{{\left(\frac{{\mu }_0}{4\pi }\frac{2i_1}{a}\right)}^2+{\left(\frac{{\mu }_0}{4\pi }\frac{2i_2}{a}\right)}^2}$
$=\frac{{\mu }_0}{2\pi a}(i_1^2+i_2^2{)}^{\frac{1}{2}}$