All Problems

Conductors and Dielectrics in an Electric Field

Problem 3.65

A system consists of two concentric conducting spheres, with the inside sphere of radius \(a\) carrying a positive charge \(q_{1}\) What charge \(q_{2}\) has to be deposited on the outside sphere of radius \(b\) to reduce the potential of the inside sphere to zero? How does the potential \(\varphi\) depend in this case on a distance \(r\) from the centre of the system? Draw the approximate plot of this dependence.

Reveal Answer
q2=−baq1;φ=q14πε0×{1/r−1/a if a⩽r⩽b(1−b/a)r if r⩾bq_{2}=-\frac{b}{a} q_{1} ; \quad \varphi=\frac{q_{1}}{4 \pi \varepsilon_{0}} \times\left\{\begin{array}{l} 1 / r-1 / a \text { if } a \leqslant r \leqslant b \\ (1-b / a) r \text { if } r \geqslant b \end{array}\right.
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