Problem 3.66

Four large metal plates are located at a small distance \(d\) from one another as shown in Fig. 3.8. The extreme plates are interconnected by means of a conductor while a potential difference \(\Delta \varphi\) is applied to internal plates. Find: (a) the values of the electric field strength between neighbouring plates; (b) the total charge per unit area of each plate.

Reveal Answer

\begin{aligned} & 3.66 .(a) E_{23}=\Delta \varphi / d, E_{12}=E_{34}=1 / 2 E_{23} ; \text { (b) }\left|\sigma_{1}\right|=\sigma_{4}=\\ =& 1 / 2 \varepsilon_{0} \Delta \varphi / d, \sigma_{2}=\left|\sigma_{3}\right|=3 / 2 \varepsilon_{0} \Delta \varphi / d \end{aligned}

Conductors and Dielectrics in an Electric Field