Electric Potential and Electric Energy; Capacitance

Adapted from Giancoli Physics

Potential Energy

• Measured as a difference of potential energies rather than as an absolute value.– Electric potential

energy refers to the change in potential energy as charge moves from A to B.

Electric Potential Energy

• The negative of the work done by the electric field to move the charge.

• Because it is the difference between the points that is measured, EITHER point can be zero.

Electric Potential

• V is defined as the quotient of potential energy to charge, such that

• Also, Vab= Va - Vb =

Va =Ua

q

−Wba

q*Measured In Volts

Electric Potential

•Usually called VOLTAGE.

•Electric Potential is a measure of Electric Potential Energy PER CHARGE. •V = PE/q

+ + +

More Energy Less Energy

+ + +

More EnergyPer charge

More Total Energy because more “less energy per charge” charges

Electric Potential Energy Vs. Electric Potential

+ ++ ++

+ +Higher Voltage

Lower Voltage

Voltage

• A measure of electric potential energy per unit of charge.

• 1 V = 1J/1C

• ∆U = Ub - Ua = qVba

Relation Between Potential and Field

• For a uniform electric field:

• E = Vba/d for a positive charge q moved to a point b to a point a separated by d meters.

• Electric field is a vector with units V/m or N/C

• Electric Potential is a scalar with units V or J/C

The Electron-Volt

• A unit of energy on the microscopic level.

• 1 eV = 1.6 x 10-19 J (sound familiar?)

• The energy gained or lost by an electron traveling across a 1V difference.

Electric Potential Due to Point Charges

• Assuming V = 0 when d = ∞, V at distance r from point Q is given by

• V = kQ/r

• Combined electric potential for several point charges is given by the sum of their individual potentials. – (Note that sign for each potential must

equal their charge) Hooking up batteries backward.

Electric Dipoles

• Consists of two equal but opposite point charges separated by a distance.

• Water is an electric dipole.

Capacitance

• Capacitor is a charge storing device.• Made of two conducting parallel plates

separated by a small layer of air or a thin film.

• The charge quantity on each plate Q is proportional to the Voltage applied.

Q = VC. C is Capacitance (depends on Capacitor)

• C is a function of the distance between plates and the area of each, A, such that: C = ε0A/d (ε = epsilon)

C = ε (0)A/d

• ε0 = Permittivity of free space• ε0 = 8.85 x 10-12 C2/Nm2

– Permittivity is ability of an object to hold electric energy in an electric field.

• Unit of Capacitance is C/V or the farad.

(microfarad/picofarad)

Charging a Capacitor• When a battery is

connected to a series resistor and capacitor, the initial current is high as the battery transports charge from one plate of the capacitor to the other. The charging current asymptotically approaches zero as the capacitor becomes charged up to the battery voltage. Charging the capacitor stores energy in the electric field between the capacitor plates.

Dielectrics

• Materials used to separate the plates of a capacitor.– The dielectric constant: a ratio of

Capacitance ranging from 1-10 comparing a capacitor with a material between the plates to a capacitor with a vacuum between the plates.

K =C2

C1

Some Dielectric ConstantsMaterial Dielectric Constant

(K)Proportionality

Constant (k)

Air 1.0 8.9 x 109

Paraffin 2.2 4.1 x 109

Polyethylene 2.3 3.9 x109

Rubber 2.8 3.2 x 109

Mica 6.0 1.5 x 109

Glass 8.0 1.1 x 109

Why Use a Dielectric?

• If charge grows too high between two plates, the capacitor could do damage to equipment.

• Inserting a dielectric lowers the capacitance of the conductors.

• Polarized or temporarily polar bodies lower the potential.

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The Leyden Jar

• A simple capacitor.

• Used to store and release charge.

Let’s build one!