Two metal balls of the same radius `a` are located in a homongenous poorly conducting medium with resistivity `rho`. Find the resistance of the medium between the balls provided that the separation between them is mush greater than the radius of the ball.

A metal ball of radius a is located at a distance l from an indinite ideally conducting plane. The space around the ball is filled with a homongeous poorly conducting medium with resistivity rho . In the case of a lt lt l find : (a) the current density at the conducting plane as a function of distance r from the ball if the potentail difference between the ball and the plane is equal to V , (b) the electric resistance of the medium between the balll and the plane.

A metal ball of radius a is surrounded by a thin concentric metal shell of radius b . The space between these electrodes is filled up with a poorly conducting homogenous medium of resistivity rho . Find the resistance of the interelectrode gap. Analyse the obtained solution at b rarr oo .

The space between two conducting concentric spheres of radii a and b (a lt b) is filled up with homongeneous poorly conducting medium. The capacitance of such a system equals C . Find the resistivity of the medium if the potential difference between the spheres, when they are disconnected from an external voltage , decreases eta -fold during the time interval Delta t .

Two conductors of aribitary shape are embedded into an infinite homogenous poorly conducting medium with respectivity rho and permittivity epsilon . Find the value of a product RG for this system where R is the resistance of the medium between the conductors, and C is the mutual capacitance of the wires in the presence of the medium.

The space between two concentric metallic spheres is filled up with a unifrom poorly conducting medium of resistivity rho and permittivity epsilon . At what moment t = 0 the inside sphere obtains a certain charge. Find: (a) the relation between the vectros of displacement current density and conduction current density at an arbitarry point of the medium at the same moment of time, (b) the displacement current across an arbitrary closed surface wholly located in the medium and enclosing the internal sphere, if at the given moment of time the charge of that sphere is equal to q .