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**Chapter 30. Potential and Field**

To understand the production of electricity by solar cells or batteries, we must first address the connection between electric potential and electric field. Chapter Goal: To understand how the electric potential is connected to the electric field.

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**Chapter 30. Potential and Field**

Topics: Connecting Potential and Field Sources of Electric Potential Finding the Electric Field from the Potential A Conductor in Electrostatic Equilibrium Capacitance and Capacitors The Energy Stored in a Capacitor Dielectrics

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Stop to think page 916 Stop to think page 918 Stop to think page 920 Stop to think page 922 Stop to think page 927

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**Finding the Potential from the Electric Field**

The potential difference between two points in space is where s is the position along a line from point i to point f. That is, we can find the potential difference between two points if we know the electric field. We can think of an integral as an area under a curve. Thus a graphical interpretation of the equation above is

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**EXAMPLE 30.2 The potential of a parallel-plate capacitor**

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**EXAMPLE 30.2 The potential of a parallel-plate capacitor**

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Batteries and emf The potential difference between the terminals of an ideal battery is ε-emf (electromotive force) In other words, a battery constructed to have an emf of 1.5V creates a 1.5 V potential difference between its positive and negative terminals. The total potential difference of batteries in series is simply the sum of their individual terminal voltages:

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**Finding the Electric Field from the Potential**

In terms of the potential, the component of the electric field in the s-direction is Now we have reversed Equation 30.3 and have a way to find the electric field from the potential.

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**EXAMPLE 30.4 Finding E from the slope of V**

QUESTION:

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Kirchhoff’s Loop Law For any path that starts and ends at the same point Stated in words, the sum of all the potential differences encountered while moving around a loop or closed path is zero. This statement is known as Kirchhoff’s loop law.

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**Capacitance and Capacitors**

The ratio of the charge Q to the potential difference ΔVC is called the capacitance C: Capacitance is a purely geometric property of two electrodes because it depends only on their surface area and spacing. The SI unit of capacitance is the farad: 1 farad = 1 F = 1 C/V. The charge on the capacitor plates is directly proportional to the potential difference between the plates.

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**Combinations of Capacitors**

If capacitors C1, C2, C3, … are in parallel, their equivalent capacitance is If capacitors C1, C2, C3, … are in series, their equivalent capacitance is

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**The Energy Stored in a Capacitor**

Capacitors are important elements in electric circuits because of their ability to store energy. The charge on the two plates is ±q and this charge separation establishes a potential difference ΔV = q/C between the two electrodes. In terms of the capacitor’s potential difference, the potential energy stored in a capacitor is

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**EXAMPLE 30.9 Storing energy in a capacitor**

QUESTIONS:

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**The Energy in the Electric Field**

The energy density of an electric field, such as the one inside a capacitor, is The energy density has units J/m3.

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Dielectrics The dielectric constant, like density or specific heat, is a property of a material. Easily polarized materials have larger dielectric constants than materials not easily polarized. Vacuum has κ = 1 exactly. Filling a capacitor with a dielectric increases the capacitance by a factor equal to the dielectric constant.

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**Summary: General Principles**

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