The magnitude of magnetic induction at the mid-point O due to the current arrangement shown in the figure is:
\( \frac{\mu_0 I}{2 \pi a} \)
\( \frac{\mu_0 I}{\pi a} \)
\( \frac{\mu_0 I}{4 \pi a} \)
- Magnetic field contributions due to segments \( BC \) and \( ET \) are outward at point \( O \).
Total magnetic field:
\[ B = \frac{\mu_0 I}{4 \pi r} + \frac{\mu_0 I}{4 \pi r} = \frac{\mu_0 I}{\pi a}. \]
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: