All Problems

Electric Current

Problem 3.155

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 homogeneous medium of resistivity \(\rho\). Find the resistance of the interelectrode gap. Analyse the obtained solution at \(b \rightarrow \infty\).

Reveal Answer
R=ρ(b−a)/4πab. In the case of b→∞R=ρ/4πaR=\rho(b-a) / 4 \pi a b . \text { In the case of } b \rightarrow \infty \quad R=\rho / 4 \pi a
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