Electrostatics

Transcript Electrostatics

Electrostatics

GIRL SAFELY CHARGED TO SEVERAL HUNDRED THOUSAND VOLTS GIRL IN GREAT DANGER AT SEVERAL THOUSAND VOLTS

The Nature of Electric Charge

Discovery of charge The Greeks first noticed electric charged by rubbing amber with fur, then picking up bits of matter. The Greek word for amber is elektron.

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, and protons ( electrons (

q p

)

q e

) have negative charge have positive charge.

Charge is quantized, meaning it comes in discrete amounts (like money).

total charge = integer x fundamental unit of charge

Insulators and Conductors

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.

CHARGED INSULATOR CHARGED CONDUCTOR

Polarization

Polarization is the separation of charge In a conductor, “free” electrons can move around the surface of the material, leaving one side positive and the other side negative.

In an insulator, the electrons “realign” themselves within the atom (or molecule), leaving one side of the atom positive and the other side of the atom negative.

Polarization is not necessarily a charge imbalance!

Charging by Friction

POSITIVE Rabbit's fur Glass Mica Nylon Wool Cat's fur Silk Paper Cotton Wood Lucite Wax Amber Polystyrene Polyethylene Rubber ballon Sulfur Celluloid Hard Rubber Vinylite Saran Wrap NEGATIVE When insulators are rubbed together, one gives up electrons and becomes positively charged, while the other gains electrons and becomes negatively charged.

Materials have different affinities for electrons. A triboelectric series relative affinity.

A material will give up electrons to another material below it on a triboelectric series.

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rates this Common examples of charging by friction: • small shocks from a doorknob after walking on carpet with rubber-soled shoes • plastic foodwrap that sticks to a container • sweater pulled over your head that sparks • laundry from the dryer that clings • balloon rubbed with hair sticks that to a wall

Charging by Conduction

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

CHARGING NEGATIVELY CHARGING POSITIVELY 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.

Remember, only electrons are free to move in solids.

Notice that the original charged object loses some charge.

Charging by Induction

Induction uses the influence of one charged object to “coerce” charge flow.

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 (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).

An object charged by induction has the opposite sign of the influencing body.

Notice that the original charged object does not lose charge.

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Electric Forces and Electric Fields

CHARLES COULOMB (1736-1806) MICHAEL FARADAY (1791-1867)

Electrostatic Charges

A New Fundamental Physics Quantity Electrostatic charge is a fundamental quantity like length, mass, and time.

The symbol for charge is

The SI unit for charge is called the

coulomb

(C).

ATTRACTION AND REPULSION The charge of an electron (

q e

) is -1.6 x 10 -19 C The charge of an proton (

q p

) is 1.6 x 10 -19 Common electrostatic charges are small: millicoulomb = mC = 10 -3 C microcoulomb =



C = 10 -6 nanocoulomb = nC = 10 -9 C C C

The Electrostatic Force

Charles Coulomb’s Torsion Balance A torsion balance measures the force between small charges.

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”)!

COULOMB’S LAW OF ELECTROSTATIC FORCE constant charges

F e



2 electrostatic force distance TORSION BALANCE The constant of proportionality, k, is equal to 9.0 x 10 9 Nm 2 /C 2 .

A negative force is attractive, and a positive force is repulsive.

The sign (+ or –) is different from a vector direction (left or right)

The Electrostatic Force

EXAMPLE 1 - Find the force between these two charges

F e F e

  9.0

 10 9   5  10  6 C  0.04

m  2    8  10  6 C    225 N The negative signs means force of attraction, but does not indicate left or right direction

EXAMPLE 2 - Find the net force on the left charge

F e F e

  9.0

 10 9   5  10  6 C  0.025 m  2   5  10  6 C   360 N (force of repulsion)

F net F net

 

F left



F right

360 N  225 N  135 N, to the left

The Electrostatic Force

EXAMPLE 3 - Find the net force on the upper left charge

425 N, 58˚

F e,x

 225 N, right

F e,y

 360 N, up 

F e



F e,x

2 

F e,y

2  225 2  360 2  425 N   tan  1  

F e,y



F e,x

  tan  1   360 225    58.0Þ

EXAMPLE 4 (Honors only) - Find the net force on the lower left charge

307 N, -63.4˚

F e1

  9.0

 10 9   5  10 -6 C   –8  10 -6 C  0.04

2  0.025

2 m  162   tan -1   2.5

4    32Þ

F e1,x

 162 cos 32Þ  137.2 N

F e1,y

 162 sin 32Þ  85.75 N 

F e

 

F e,x

2  

F e,y

2  137.2

2  (85.75

 360) 2  307 N   tan  1   

F e,y



F e,x

   tan  1   85.75

 137.2

360     63.4Þ

Electric Field Strength

Field Theory Visualizes Force At A Distance DEFINITION OF GRAVITATIONAL FIELD DEFINITION OF ELECTRIC FIELD g field



force mass E field



force charge



F m g E



F q

q 0

is a small, positive test charge Electric field is a vector quantity SI unit of electric field

E field points toward negative charges E field points away from positive charges newton coulomb  N C

Electric Field Lines

Single Point Charges POSITIVE CHARGE NEGATIVE CHARGE Density of field lines indicates electric field strength Inverse square law obeyed

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Definition of E Field for single point charge constant

E



F q



kq

q / r

q

0 electric field



kq r

2 charge distance

Electric Field Lines

Electric fields for multiple point charges POSITIVE AND NEGATIVE POINT CHARGES TWO POSITIVE POINT CHARGES OPPOSITE MAGNETIC POLES ALIKE MAGNETIC POLES

Electric Fields

EXAMPLE 1 Find the electric field strength at 2 meters from the 5 millicoulomb charge.



kq r

  9  10 9 Nm 2 /C 2   2   5  10  3 C 

=1.13

 10 7 N/C, to the right

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



F e F e



  1.6

 10 -19 C   1.13

 10 7 N/C   1.81

 10 -12 N, to the right

q F e

  9  10 9 Nm 2 /C 2   5  10  3 C   2   1.6

 10 -19 C   1.8

 10 -12 N, to the right

Electric Potential Energy

Electric Potential Energy versus Gravitational Potential Energy FALLING MASS VS. FALLING CHARGE STORING POTENTIAL ENERGY Electric potential energy (PE) is stored when a positive charge is moved against an electric field.

Potential energy can be converted to kinetic energy, heat, light, sound etc.

POTENTIAL ENERGY GAIN OR LOSS toward E positive (+) charge

loses

negative ( –) charge

gains

Potential energy is a scalar quantity measured in joules (J).

opposite E

gains

loses

for Constant Electric Field

CONSTANT GRAVITATIONAL FIELD CONSTANT ELECTRIC FIELD



mgh PE



qEd

electric potential energy charge Example How much potential energy is converted when an electron is accelerated through 0.25 m in a cathode ray tube (TV set) with an electric field strength of 2 x 10 5 N/C?

E field distance



qEd

 (  1.6

 10  19 ) (2  10 5 )(0.25)  8.0

 10  15 J

for Two Point Charges (Honors only)

Potential Energy is force times distance constant charges



F e d



2 

r PE

electric potential energy Potential energy is positive for like charges Potential energy is negative for opposite charges Potential energy is zero at infinite distance



distance Example How 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).



 (9  10 9 )(1.6

 10  19 )(–1.6

5.3

 10  11  10  19 )   4.35

 10  18 J

Potential Difference (Voltage)

Electric potential is average energy per charge.

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

Potential



A good analogy:

potential potential energy

is to

heat

is to

temperature

, as





Energy Charge



PE q

Potential difference is often called voltage .

Voltage is only dangerous when a lot of energy is transferred.

SI Units

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Voltage, like energy, is a scalar.

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 V  J C

source

common dry cell car battery household (US) comb through hair utility pole transmission line Van de Graaff lightning

voltage (V)

1.5

12 120 500 4,400 120,000 400,000 1,000,000,000

Potential Difference (Voltage)

A SEVERAL THOUSAND VOLT POWERLINE CAN ILLUMINATE A FLUORESCENT LIGHT A PARACHTUE ACCIDENT LANDED THIS MAN ON A 138,000 THOUSAND VOLT LINE, BUT HE SUFFERED ONLY MINOR BURNS

Potential Difference for Constant Electric Field

Potential energy is often stored in a capacitor.

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

Most capacitors have constant electric fields.



 



q qEd q





voltage E field distance Example Calculate the magnitude of the electric field set up in a 2-millimeter wide capacitor connected to a 9-volt battery.



 9 

(0.002) 

 4500 N/C

Potential Difference for Point Charge (Honors only)

Consider a test charge to measure potential



kqq

0 /

r q 0

Example -4 nC find ∆ here 0.3 m 10 nC 0.4 m 6 nC

potential difference constant





kq r

charge distance



1 

2  

kq r kq r

1 2   (9 (9 

3 



kq r

 

1 3  (9  

2   10 10   9 9

)(6 0.3

)( 3  0.5

  0.4

 10 9 )(10 4 10   180  10 10 9   )  9 9 )  ) 90 180 V     90 V 180 V 180  270 V

Summary of Electrostatic Equations

Electrostatic Force

F e



force between two charges Potential Energy



qEd

for constant E field Electric Field



for two charges Honors only!



F q

definition



kq r

for point charge Potential Difference



 

PE q

definition





kq r

for point charge





for constant E field