A short magnet oscillates with a time period 0.1 s at a place where horizontal magnetic field is $24 \mu \mathrm{~T}$. A downward current of 18 A is established in a vertical wire kept at a distance of 20 cm east of the magnet. The new time period of oscillations of the magnet is

Two toroids with number of turns 400 and 200 have average radii respectively 30 cm and 60 cm . If they carry the same current, the ratio of magnetic fields in these two toroids is

Three rings, each with equal radius $r$ are placed mutually perpendicular to each other and each having centre at the origin of coordinate system. $I$ is current passing through each ring. The magnetic field value at the common centre is

A proton and an alpha particle moving with energies in the ratio $1: 4$ enter a uniform magnetic field of 3 T at right angles to the direction of magnetic field. The ratio of the magnetic forces acting on the proton and the alpha particle is