The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively, $$1.0 \times 10^{-2} \mathrm{~A} \mathrm{~m}^2$$ and $$\frac{10^{-6}}{\pi^2} \mathrm{~kg} \mathrm{~m}^2$$. If it completes 10 oscillations in $$10 \mathrm{~s}$$, the magnitude of the magnetic field is

The magnetic moment of an iron bar is $$M$$. It is now bent in such a way that it forms an arc section of a circle subtending an angle of $$60^{\circ}$$ at the centre. The magnetic moment of this arc section is

In a uniform magnetic field of $$0.049 \mathrm{~T}$$, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $$9.8 \times 10^{-6} \mathrm{~kg} \mathrm{~m}^2$$. If the magnitude of magnetic moment of the needle is $$x \times 10^{-5} \mathrm{~Am}^2$$, then the value of '$$x$$' is :

In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions: