Question

Two concentric circular loops of radii R and 2R carry current of $2i$ and $i$ respectively in opposite sense. The resultant magnetic field at their common center is.

• A. ${\mu }_0\frac{i}{4R}$
• B. ${\mu }_0\frac{5i}{4R}$
• C. ${\mu }_0\frac{3i}{4R}$
• D. ${\mu }_0\frac{i}{2R}$

Answer 1

The correct option is C ${\mu }_0\frac{3i}{4R}$

Concept :

$Magneticfieldaroundcircularloop=\frac{U_{0}I}{2R}$

Solution:

$MagneticField,B_1=\frac{U_0\times 2\times I}{2\times R}$

$Similarly,MagneticField,B_2=\frac{U_0\times I}{2\times \left(2R\right)}$

Net magnetic field,B = $B_1-B_2$

$\Rightarrow B=\frac{U_0\times I}{R}-\frac{U_0\times I}{4R}$

$\Rightarrow B=\frac{U_{0}I\times 3}{4R}$

Hence, option C is correct.