Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of $${{{\mu _0}I} \over \pi }$$ is :

The figure shows a region of length ‘l’ with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 $$ \times $$ 10⁵ ms^–1 making an angle 60^o with the field. If the proton completes 10 revolution by the time it cross the region shown, ‘l’ is close to
(mass of proton = 1.67 $$ \times $$ 10^–27 kg, charge of the proton = 1.6 $$ \times $$ 10^–19 C)

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is

A beam of protons with speed 4 × 10⁵ ms^–1 enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to :
(Mass of the proton = 1.67 $$ \times $$ 10^–27 kg, charge
of the proton = 1.69 $$ \times $$ 10^–19 C)