A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.34). Show that the capacitance of a spherical capacitor is given by
`C = (4 pi epsilon_(0)r_(1)r_(2))/(r_(1)-r_(2))`

where `r_(1)` and `r_(2)` are the radii of outer and inner spheres, respectively.

The capacitor C of a spherical conductor of radius R is proportional to

If in a triangle (r)/(r_(1)) = (r_(2))/(r_(3)) , then

The mutual inductance between two planar concentric rings of radii r_(1) and r_(2)(r_(1) > r_(2)) placed in air is given by:

The radii of the bases of two right circular solid cones of same height are r_(1) and r_(2) respectively. The cones are melted and recast into a solid sphere of Radius ''R'' show the height of the cone is given by h=(4R^(3))/(r_(1)^(2)+r_(2)^(2)

A charge Q is distributed over two concentric hollow spheres of radii r and R (R gt r), so that the surface charge densities are equal. The potential at the common centre is (1)/(4pi epsi_(0))" times"

The inner and outer radii of a spherical capacitor are r_1 and r_2 respectively. When the inner surface is earthed . The outer sphere is given a charge +Q , then the charge on the inner surface is

A hemispherical solid of radius r_1 units is melted and made into 32 identical spherical balls each of radius r_2 units then r_1 : r_2 is:

The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

A spherical capacitor has an inner sphere of radius 12cm and an outer sphere of radius 13cm. The outer sphre is earthed the inner sphere is given a charge of 2.5muC . The space between the concentric spheres is filled with a liquid of dielectric constant 32. a. Determine hte capacitance of the capacitor. b. What is the potential of hte inner sphere? c. Compare the capacitance of this capacitor with that of an isolated sphere of radius 12cm. Explain why the latter is much smaller.