Chapter 16Electrical Energyand Capacitance

Electrical PotentialReminder from physics 1:

Work done by a conservative force, depends only on the initial and final positions.

Work is “path independent”.

Produces: Potential energy

Examples: gravitational potential energyelastic (spring) potential energy

Both the coulomb force and the gravitational force are proportional to 1/r2.

Both are examples of a “central” force.Both of these forces are conservative forces.

When you do work against gravity, you changed the gravitational potential energy.

Doing work against the Coulomb force (electric force) changes the electrical potential energy.

Work and potential energy

Work done by a force to move an object is the product of the component of the force parallel to the displacement and the displacement.

W = F d cos θ

in figure 16.1 Wab= Fx∆x= qEx(xf–xi)

This is the work that moves a charge from A to B.

Work and EnergyReminder from physics 1:

Work-Energy Theorem: Wnet = ∆KE

From ch 5, the work done by a conservative force is equal to the negative of the change in potential energy associated with the force.

For a charge in an electric field:∆PE = -WAB= -qEx∆x

In fig. 16.1, as the positive charge moves from left to right, positive work is done on the charge, the charge loses some electrical potential energy.

(Note that this equation is valid when the field is constant.)

See also figure 16.2

Conservation of Energy∆KE + ∆PE = 0

As a charge moves through an electric field, it will gain or lose electric potential energy.

The change will be equal to the change in kinetic energy.

Can repeat the situation with a negative charge.

If released from rest the negative charge will move in the opposite direction that the positive charge traveled.

A positive charge loses potential energy as it travels along the electric field.

Opposite for a negative charge.

work example 16.1 a

Chapter 15

This leads us to the concept of electrical potential difference. (Usually called potential difference)

... and voltage.

If release a mass is the presence of a gravitational field, it will naturally travel from region of high potential to low potential.

Ex. Let a ball roll down a hill.If you release a positive charge from rest, it will accelerate from a region of higher potential to a region of lower potential.

If you release a negative charge from rest, it will accelerate from a region of lower potential to a region of higher potential.

TV tube example

A proton is injected between two parallel plates with a speed of 1x106m/s. The plates are 5 cm apart.

a) what must be the potential difference if the proton is to exit with a speed of 3x106m/s?

b) What is the magnitude of the electric field between the two plates.

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Electrical Potential for Point Charges

Fig 16.5

What happens when we introduce a proton and an electron and let them go?

If you have two or more charges, you can find the electric potential via the superposition principle.

Find the potential from each charge and add up the values.

Potential is a scalar, so no need to worry about vectors and direction this time.

Fig. 16.6 shows the potential of an electric dipole.

-W

No work is needed to move a charge around inside a conductor.

The

Electron VoltWe want to have a conveniently sized unit of energy.An electron volt is the kinetic energy that an electron gains when accelerated through a potential difference of 1V.1V = 1 J/C

Magnitude of charge of electron = 1.6x10-19C1eV = (1.6x10-19C ) (1V) = 1.6x10-19J

This is convenient because 1 J is a lot of energy to give an electron.

Application Van de graaf generator/accelerator

Van de graaf acceleratorUses principles from chapters 15, 16 to accelerate charged particles.

Capacitancecapacitor– Electrical device used in many circuits that is used to store electrical energy to be used later.

Consists of two conductors separated from each other.

Example: parallel plate capacitor. Two parallel metal plates separated by distance, d, and connected to positive and negative terminals of a battery. One plate loses electrons and receives a charge of +Q. The electrons are transferred through the battery to the other plate which obtains a charge of -Q.

For

See fig 16.15 for electric field of parallel plate capacitor.Applications:

Camera flashKeyboardTiming devices

We can combine capacitors in the following configurations:

:

For two capacitors, we found:Ceq= C1+ C2

We can extend this to more capacitors.Ceq= C1 + C2 + C3 + C4 + ……The total capacitance of capacitors in parallel is the sum of the capacitances.Thus the equivalent capacitance is larger than any of the individual capacitances.(Electrical devices in parallel have the same potential difference across each device.)

:

Energy stored in a capacitorCapacitors store electrical energyThat amount of energy is the same as the magnitude of work required to move charge, Q, onto the plates of the capacitor.When a capacitor discharges, it releases the energy (sparks).

Find out how much work is required to charge a capacitor.

As more and more charge is place on a capacitor, the voltage between the capacitor’s plates increases.

It requires more and more work to add each additional charge.See figure 16.23

Total work to fully charge the capacitor is the area under the graph.In this case, the area of the triangle whose base and height are Q and ∆V.

Substituting Q =C∆V, yields Energy stored = ½ C(∆V)2 = ½ Q2/C

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Dielectric – An insulating material, such as plastic, that can be inserted into a capacitor to change the capacitance without changing the geometry of the capacitor.

If the dielectric completely fills the capacitor, the capacitance is multiplied by the dielectric constant (κ).

Atomic description of a dielectric, fig 16.33

Dielectric strength – the maximum electric field that can be produced in a dielectric before it breaks down and begins to conduct.

For air the dielectric strength is about 3x106 V/m.

Capacitors with multiple dielectrics

See examples on page 588.

Dielectric strength of air is about 3x106 V/m.

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