Chapter 18 – Electric Potential and Capacitance

Section 1

Electric Potential Energy

Electric Potential Energy

• Electric Potential Energy is a form of mechanical energy, which is conserved

• Any time a charge moves within an electric field, work is done on that charge

• If a positive charge moves in the direction of the electric field, it will lose PEe; if a negative charge moves in the direction of the electric field, it will gain PEe….WHY?

What is a Uniform Electric Field?

• Exists where the electric field lines are parallel and evenly spaced

• Direction of the field is determined by which way a small positive test charge will move if free to do so

++++++++

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+

• Compare a charge moving through a uniform electric field and a ball moving through a gravitational field:

ballpositive charge

Earth

The ball loses gravitational potential energy as it falls toward the Earth

What determines the direction of an electric field?

The charge loses electrical potential energy as it “falls” in a uniform electric field

(-)

negative

(+)

positive

Electric Potential Energy in a Uniform Electric Field

PEelectric = -qEd

Electric Potential Energy = -(charge x electric field strength x displacement from

a reference point in the direction of the field)

Electric Potential Energy for a pair of charges

PEelectric = kc q1q2

rThese energies can be added together

using algebraic summation – these are scalar quantities!

Chapter 18 – Electric Potential and Capacitance

Section 2

Potential Difference

Potential Difference

• Electric Potential Difference is a change in electric potential – a change in the ability to do work:

∆V = PEelectric

q SI unit is the Volt = Joule/Coulomb

As a 1 coulomb charge moves through a potential difference of 1 volt, the charge loses (or gains) 1 joule of energy

Examples• Batteries: the difference

between the two terminals on a battery ranges from 1.5 volts to 12 volts – as charges move from one terminal to another, the energy can be used for work, like water falling over a water mill is used to do work

• Household electrical outlet is 120 volts

Potential Difference in a Uniform Electric Field

∆V = -E∆d∆d is the displacement in the direction of the

electric field; perpendicular movement in an electric field does not change the electric potential difference. Why is there a negative sign here?

(Remember the equation for E? It’s from chapter 17: E = kcq1/r2)

Potential difference between a point at infinity and a point near a

point charge

• Huh? Don’t stress over this too much, look at the explanation on pg. 672

∆V = kc q

r

Vectors in Electric Potential?

• No, these are scalar quantities!

• Simply add the Electrical Potentials, paying attention to the signs, to get the algebraic sum

A battery does work to move charges!• Inside a 12 volt battery, the electric field does 12 joules

of work to move a 1 Coulomb charge from the (-) terminal to the (+) terminal

• when you connect your device to this battery, the charge moves from the (+) terminal, through the device toward the (-) terminal, and gives up the 12 joules of energy to power your device.

• When it reaches the (-) terminal, the charge has an electric potential of zero again, and the battery does 12 more joules of work on the charge to get it back to the (+) terminal, ready for another round trip through your device.

Chapter 18 – Electric Potential and Capacitance

Section 3 - Capacitance

Capacitors and Charge Storage

• A parallel plate capacitor consists of two parallel metal plates separated by a non-conducting material, then rolled into a cylinder. One plate is attached by a conducting wire to the (-) terminal of a battery, the other plate is attached to the (+) terminal of the battery

• The difference in potential energy in the battery causes opposite charges to build up on the plates, so that eventually the potential difference between the plates is equal to the potential difference between the battery terminals

• In this way, the capacitor can store charges and their potential energy away from the battery

• The “capacitance” of a conductor is its ability to store energy in the form of electrically separated charges

C = Q capacitance = charge on plate ∆V potential difference

SI unit for capacitance is the farad (F) = Coulombs/voltTypical values range from 1 µF to 1 pF

Capacitance for a parallel plate capacitor in a vacuum

C = ε0 A d

Capacitance = permittivity of a vacuum x area of one plate distance between the plates

The capacitance of a sphere increases with its radius; for example, earth has an extremely large capacitance, so it can provide or accept a large amount of charge without its electric potential changing very much; this is why the earth is used as a ground in electric circuits.

The material between the plates of a capacitor can change its capacitance

• A material called a “dielectric” is used to improve capacitance

• A “dielectric” is an insulator (rubber, glass, etc) that is inserted between the plates of a capacitor, which allows charges to accumulate on the surface of the plate. A vacuum can’t do this. This allows the capacitor to store more charge for a given potential difference, increasing the conductor’s capacitance

Discharging capacitors rapidly release their charge

• Once the capacitor is charged, the battery can be removed from the circuit and the capacitor will remain charged as long as it is not connected to a conductor.

• Once the plates are connected to a conductor, the capacitor will discharge – the charges move back from one plate to the other until there is zero potential difference between them

• This allows an instantaneous release of the energy stored in the capacitor, which has many applications – camera flashes for example.

Capacitor uses

• Also, the potential energy stored can be manipulated by bringing the plates closer to each other, which can be detected. Some types of keyboards use this.

• Finally, since the area of the plates and the distance between them can be controlled, the capacitance, and thus the electric field strength, can also be easily controlled

Energy and Capacitors

• A capacitor stores electrical potential energy because it requires work to move charges through a circuit to the opposite plates of a capacitor. The work done is a measure of the transfer of energy

Equations for Electrical Potential Energy stored in a capacitor

PEelectric = ½ Q∆V

PEelectric = ½ C(∆V)2

PEelectric = Q2

2C

PEelectric = electric potential energy in Joules

Q = charge on one plate in Coulombs

∆V = change in potential difference in Volts

C = capacitance of the conductor in Coulombs/Volt (farad – F)