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`.

Explanation

Let us mentally isolate a thin spherical layer of inner and outer radii `r` adn `r + dr` Lines of current at all the points of the this layer are perpendicular to it and therefore such a layer can be treated as a spherical conductor of thinkness `dr` and cross sectional area `4pi r^(2)`. So
`dR = rho (dr)/(4pi r^(2))` ...(1)
And intergating (1) between the limits [a,b] we get,
`R = (rho)/(4pi) [(1)/(a) - (1)/(b)]`
Now, for `b rarr oo`, we have
`R = (rho)/(4pi a)`