Question

Two straight long conductors AOB and COD are perpendicular to each other and carry currents $I_1$ and $I_2$. The magnetic induction at a point P at a distance d from the point O in a direction perpendicular to the plane ABCD is :

• A. $\frac{{\mu }_0}{2\pi d}(I_1+I_2)$
• B. $\frac{{\mu }_0}{4\pi d}(I_1-I_2)$
• C. $\frac{{\mu }_0}{2\pi d}(I_1^2+I_2^2{)}^{1/2}$
• D. $\frac{{\mu }_0}{2\pi d}\frac{I_1{I}_2}{I_1+I_2}$

Answer 1

Answer: (C)

$\frac{{\mu }_0}{2\pi d}(I_1^2+I_2^2{)}^{1/2}$

B due to first conductor at a distance d,
$B_1=\frac{{\mu }_0{I}_1}{2\pi d}$
B due to second conductor at a distance d,
$B_2=\frac{{\mu }_0{I}_2}{2\pi d}$
$B_1$ & $B_2$ are perpendicular to each other
So,
$B_{net}=\sqrt{{B_1}^2+{B_2}^2}$
$=\frac{{\mu }_0}{2\pi d}({I_1}^2+{I_2}^2{)}^{\frac{1}{2}}$