A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is :
$$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}Tm{{A}^{-1}}} \right)$$

A cylinderical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field. B with the distane d from the centre of the conductor, is correctly represented by the figure :

Ionized hydrogen atoms and $$\alpha $$-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths r_H : r_{$$\alpha $$} will be :

A metallic rod of mass per unit length 0.5 kg m^–1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is