Electrostatics for M.6

Electrostatics

Teacher : Piyanuch Plaon

Subject : Physics 4

Discovery of charge

Benjamin Franklin arbitrarily called the two kinds of charge positive and negative. In most cases, only the negative charge is mobile.

Properties of charge

Like charges repel, and unlike charges attract.

Charge is conserved, meaning it cannot be created or destroyed, only transferred from one location to another.

In all atoms, electrons have negative charge and protons have positive charge.

Insulators

In insulators, electrons are bound in “orbit” to the nucleus in each atom.When charge is placed on an insulator, it stays in one region and does not distribute.Wood, plastic, glass, air, and cloth are good insulators.

Conductors

In conductors electrons can move from atom to atom, thus electricity can “flow”. When charge is placed on a conductor, it redistributes to the outer surface.Metals (copper, gold, and aluminum) are good conductors.

Charging by Friction When insulators are

rubbed together, one gives up electrons and becomes positively charged, while the other gains electrons and becomes negatively charged.

Charging by Conduction When a charged conductor

makes contact with a neutral conductor there is a transfer of charge.

Electrons are transferred from the rod to the ball, leaving them both negatively charged.

Electrons are transferred from the ball to the rod, leaving them both positively charged.

CHARGING NEGATIVELY

CHARGING POSITIVELY

Step 1. A charged rod is brought near an isolated conductor. The influence of the charge object polarizes the conductor but does not yet charge it.

Step 2. The conductor is grounded to the Earth, allowing charge to flow out between it and the Earth.

Charging by Induction

Charging by Induction (cont.)

Step 3. The ground is removed while the charge rod is still nearby the conductor.

Step 4. The rod is removed and the conductor is now charge (opposite of rod).

Electric Forces and Electric Fields

CHARLES COULOMB(1736-1806)

MICHAEL FARADAY(1791-1867)

Electrostatic Charges

The charge of an electron (qe) is -1.6 x 10-19 CThe charge of an proton (qp) is 1.6 x 10-19 C

Electrostatic charge is a fundamental quantity like length, mass, and time.The symbol for charge is q. The SI unit for charge is called the coulomb (C).ATTRACTIO

N AND

REPULSION

The Electrostatic Force

The constant of proportionality, k, is equal to 9.0 x 109 Nm2/C2.

COULOMB’S LAW OF

ELECTROSTATIC FORCE

Fe kq1q2

r2

constant

distance

charges

electrostatic force

The electrostatic force depends directly on the magnitude of the charges. The force depends inversely on the square of distance between charges (another “inverse square law”)!

Electric Field Strength

g Fgm

E Feq0

DEFINITION OF

GRAVITATIONAL FIELD

DEFINITION OF

ELECTRIC FIELD

g field force

massE field

force

charge

SI unit of electric fieldnewton

coulomb

N

C

Electric field is a vector quantityE field points toward negative charges

E field points away from positive charges

q0 is a small, positive test

charge

Electric Field Lines

Density of field lines indicates electric field strengthDefinition of E Field for

single point charge

POSITIVE CHARGE

NEGATIVE CHARGE

E Feq0

kq0q / r

2

q0 E kq

r2

constant

distance

charge

electric

field

Single Point Charges

Electric Field LinesElectric fields for

multiple point charges

POSITIVE AND NEGATIVE POINT

CHARGES

TWO POSITIVE POINT

CHARGES

E kq

r2

EXAMPLE 1

EXAMPLE 2

E 9 109 Nm2 /C2 5 10 3 C

2 m 2

Electric Fields

Find the force on an proton placed 2 meters from the 5 millicoulomb charge in the problem above.E

Feq

Fe qE 1.6 10-19 C 1.13107 N/C 1.8110-12 N, to the right

Fe 9 109 Nm2 /C2 5 10 3 C 1.6 10-19 C

2 m 2 1.8 10-12 N, to the right

OR

Find the electric field strength at 2 meters from the 5 millicoulomb charge.

E=1.13107 N/C, to the rightE

PE for Two Point Charges

PE kq1q2

r

Potential energy is zero at infinite distance

Potential energy is positive for like chargesPotential energy is negative for opposite charges

Potential Energy is force times distancePE Fed

kq1q2

r2r

charges

distance

electric

potentialenergy

constant

ExampleHow much electrostatic potential energy in a

hydrogen atom, which consists of one electron at a distance of 5.3 x 10-11 meters from the nucleus (proton).PE

kq1q2

r

(9 109 )(1.6 10 19 )(–1.6 10 19 )

5.310 11 4.35 10 18 J

Potential Difference (Voltage)

Potential Energy

Charge

V PEq

A volt (v) is the unit for voltage named in honor of Alessandro Volta, inventor of the first battery.1 volt

1 joule

1 coulomb

SI Units

source voltage (V)

common dry cell 1.5

car battery 12

household (US) 120

comb through hair 500

utility pole 4,400

transmission line 120,000

Van de Graaff 400,000

lightning 1,000,000,000

V J

C

A good analogy: potential is to temperature, as potential energy is to heat.

Electric potential is average energy per charge.

Potential difference is often called voltage.

Energy is a relative quantity (absolute energy doesn’t exist), so the change in electric potential, called potential difference, is meaningful.

Voltage is only dangerous when a lot of energy is transferred.Voltage, like energy, is a scalar.

Potential Difference for Constant Electric Field

V EdV PEq

qEd

q

voltage

E field

distance

Potential energy is often stored in a capacitor.

Most capacitors have constant electric fields.

Capacitors are made by putting an insulator in between two conductors.

Example

Calculate the magnitude of the electric field set up in a 2-millimeter wide capacitor connected to a 9-volt battery.V Ed 9 E(0.002) E 4500 N/C

Consider a test charge to measure potential

Potential Difference for Point Charge

V kq

r

charge

distance

potential

difference

constant

V PE

q0

kqq0 / r

q0

Example

V1 kq1

r

(9 109 )(6 10 9 )

0.3180 V

V2 kq2

r

(9 109 )( 4 10 9 )

0.4 90 V

V3 kq3

r

(9 109 )(10 10 9 )

0.5180 V

V V1 V2 V3 180 90 180 270 V

-4 nC

10 nC 6 nC

0.3 m0.4 m

find ∆V

here

CAPACITORS A basic capacitor has two parallel plates separated by an insulating material

A capacitor stores an electrical charge between the two plates

The unit of capacitance is Farads (F)

Capacitance values are normally smaller, such as µF, nF or pF

Basic capacitor construction

Dielectric material

Plate 1

Plate 2

The dielectric material is an insulator therefore no current flows through the capacitor

CAPACITORS

Storing a charge between the plates

Electrons on the left plate are attracted toward the positive terminal of the voltage source

This leaves an excess of positively charged holes

The electrons are pushed toward the right plate

Excess electrons leave a negative charge

+ -

+ _+ _

CAPACITORS

Types of capacitors The dielectric material determines the type of capacitor

Common types of capacitors are:MicaCeramicPlastic film

CAPACITORS

Variable capacitors are used in communication equipment, radios, televisions and VCRs

They can be adjusted by consumers by tuning controls

Trimmers are internal adjusted capacitors that a consumer cannot adjust

CAPACITORS

Fringing – At the edge of the capacitor plates the flux lines extend outside the common surface area of the plates.

CAPACITANCE

THE CURRENT : IC

Current ic associated with the capacitance C is related to the voltage across the capacitor by

Where dvc/dt is a measure of the change in vc in a vanishingly small period of time.

The function dvc/dt is called the derivative of the voltage vc with respect to time t.

CAPACITORS IN SERIES AND PARALLEL

- Capacitors, like resistors, can be placed in series and in parallel.- When placed in series, the charge is the same on each capacitor.

CAPACITORS IN SERIES AND PARALLEL

Placing capacitors in parallel the voltage across each capacitor is the same.

The total charge is the sum of that on each capacitor.