An air filled cylindrical capacitor (capacitance ) of length , with  and  as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity  is inserted inside  of the annular region as shown in Fig. (ii). The value of  for which the capacitance of the capacitor in Fig. (ii), becomes  is

The given equation represents a magnetic field strength  in the spherical coordinate system, in free space. Here,  and  represent the unit vectors along  and , respectively. The value of  in the equation should be ________ (rounded off to the nearest integer).        

In the figure, the electric field  and the magnetic field  point to  and  directions, respectively, and have constant magnitudes. A positive charge '  ' is released from rest at the origin. Which of the following statement(s) is/are true.

An infinite surface of linear current density  exists on the  plane, as shown in the figure. The magnitude of the magnetic field intensity  at a point  due to the surface current in Ampere/meter is __________ (Round off to 2 decimal places).