Two concentric thin circular rings of radii 50 cm and 40 cm , each carry a current of 3.5 A in opposite directions. If the two rings are coplanar, the net magnetic. field due to the two rings at their centre is

• Correct answer
  A

  $11 \times 10^{-7} \mathrm{~T}$
• B

  $22 \times 10^{-7} \mathrm{~T}$
• C

  $17 \times 10^{-7} \mathrm{~T}$
• D

  $8 \times 10^{-7} \mathrm{~T}$

Solution

$\mathrm{r}_1=40 \mathrm{~cm}, \mathrm{r}_2=50 \mathrm{~cm}, \mathrm{I}=3.5 \mathrm{~A}$
The magnitude of magnetic field at the centre O of ring, $\begin{aligned} & B=\frac{\mu_0 I}{2}\left(\frac{1}{r_1}-\frac{1}{r_2}\right) \\ & =\frac{4 \pi \times 10^{-7} \times 3.5}{2}\left(\frac{1}{40}-\frac{1}{50}\right) \times 10^2 \\ & =10.99 \times 10^{-7} \approx 11 \times 10^{-7} \mathrm{~T} \end{aligned}$

Hence, the correct answer is option: 'A'.