A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $${x \over {15}}{{{ \in _0}A} \over b}$$. The value of x is ____________.

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 __________.