The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 $$\times$$ 10⁶ A/m². The current through the outer portion of the wire between radial distances $${r \over 2}$$ and r is x$$\pi$$ A; where x is __________.

In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be $$\sqrt {{x \over 2}} $$. The value of x is __________.

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If r_d and r_p are the radii of their circular paths respectively, then the ratio $${{{r_d}} \over {{r_p}}}$$ will be $$\sqrt{x}$$ : 1 where x is __________.

A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is 4 $$\times$$ 10^$$-$$3 T and the angle of dip is 45$$^\circ$$. The emf induced in the rod is ___________ mV.