At a certain place the angle of dip is 30$$^\circ$$ and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at that certain place, is :

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 $$\times$$ 10^$$-$$5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m, is :

[Permeability of free space $$\mu$$₀ = 4$$\pi$$ $$\times$$ 10^$$-$$7 Wb/A-m]

A bar magnet having a magnetic moment of 2.0 $$\times$$ 10⁵ JT^$$-$$1, is placed along the direction of uniform magnetic field of magnitude B = 14 $$\times$$ 10^$$-$$5 T. The work done in rotating the magnet slowly through 60$$^\circ$$ from the direction of field is :