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:
\[ B = \frac{\mu_0 I}{4 \pi r} + \frac{\mu_0 I}{4 \pi r} = \frac{\mu_0 I}{\pi a}. \]
A coil of area A and N turns is rotating with angular velocity \( \omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \( \vec{B}\) Magnetic flux \(\varphi \text{ and induced emf } \varepsilon \text{ across it, at an instant when } \vec{B} \text{ is parallel to the plane of the coil, are:}\)

Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to:
