The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $r_1=3.14 \mathrm{~m}$ and $r_2=6.28 \mathrm{~m}$ and carrying a current of $\mathrm{I}=2 \mathrm{~A}$ is:

In a particular case X , a certain length of insulated copper wire is bent to form double loops of equal radii. In another case Y the same copper wire is bent to form three loops of equal radii. If the same steady current is passed through the copper wire in both the cases, the ratio of magnetic field at the centre in the case X to that in case Y is:

A straight wire of mass 250 g and length 2.5 m carries a current of 4 A . It can be suspended in mid air by a uniform horizontal magnetic field of magnitude:

A current carrying closed loop in the form of a right isosceles triangle XYZ is placed in a uniform magnetic field $B$ acting along $X Y$ of the loop. If the magnetic force on the arm $Y Z$ is $\sqrt{2} F$, then the force on the arm $X Z$ is: