A battery produces a specified potential difference ΔV between conductors attached to the battery terminals. A 12-V battery is connected between two parallel plates, as shown in Figure 25.5. The separation between the plates is d = 0.30 cm, and we assume the electric field between the plates to be

Question

A battery produces a specified potential difference ΔV between conductors attached to the battery terminals. A 12-V battery is connected between two parallel plates, as shown in Figure 25.5. The separation between the plates is d = 0.30 cm, and we assume the electric field between the plates to be uniform. (This assumption is reasonable if the plate separation is small relative to the plate dimensions and if we do not consider locations near the plate edges.) Find the magnitude of the electric field between the plates.

Accepted Answer

The electric field is directed from the positive plate (A) to the negative one (B), and the positive plate is at a higher electric potential than the negative plate is. The potential difference between the plates must equal the potential difference between the battery terminals. We can understand this by noting that all points on a conductor in equilibrium are at the same electric potential; no potential difference exists between a terminal and any portion of the plate to which it is connected. Therefore, the magnitude of the electric field between the plates is, from Equation 25.6,

[latex] \Delta V=-E \int_{A}^{B} d s=-E d [/latex] (25.6).

[latex] E=\frac{\left|V_{B}-V_{A} ight|}{d}=\frac{12 V }{0.30 imes 10^{-2} m }=4.0 imes 10^{3} V / m [/latex].

The configuration of plates in Figure 25.5 is called a parallel-plate capacitor, and is examined in greater detail in Chapter 26.

Question 25.1: A battery produces a specified potential difference ΔV betwe...

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