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

A transformer with toroidal core of permeability  is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius, and neglecting any leakage flux, the best estimate for the mean radius R is

A solid iron cylinder is place in region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will

A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the relative permeability  of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is _____________.