Two identical small bar magnets each of dipole moment $3 \sqrt{5} \mathrm{~J} / \mathrm{T}$ are placed at a center to center separation of 10 cm , with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is $\alpha \times 10^{-3} \mathrm{~T}$. The value of $\alpha$ is $\_\_\_\_$

$$ \left(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}\right) $$

A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 Gauss, experiences a torque of $0.016 \mathrm{~N} . \mathrm{m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .

The coercivity of a magnet is $$5 \times 10^3 \mathrm{~A} / \mathrm{m}$$. The amount of current required to be passed in a solenoid of length $$30 \mathrm{~cm}$$ and the number of turns 150, so that the magnet gets demagnetised when inside the solenoid is ________ A.

The horizontal component of earth's magnetic field at a place is $$3.5 \times 10^{-5} \mathrm{~T}$$. A very long straight conductor carrying current of $$\sqrt{2} \mathrm{~A}$$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is __________ $$\times 10^{-6} \mathrm{~N} / \mathrm{m}$$.