coulomb’s law physics 12. electroscope ► draw a diagram showing the forces that exist on the...

Coulomb’s LawCoulomb’s Law

Physics 12Physics 12

ElectroscopeElectroscope

►Draw a diagram showing the forces Draw a diagram showing the forces that exist on the leaves of the that exist on the leaves of the electroscope when it is placed close to electroscope when it is placed close to the Van de Graff generatorthe Van de Graff generator

Coulomb’s PendulumCoulomb’s Pendulum

► Consider the following Consider the following pendulumpendulum

► The mass initially shares The mass initially shares charge with an identical charge with an identical spheresphere

► The two spheres then have The two spheres then have identical charge and (in this identical charge and (in this case) the second sphere is case) the second sphere is moved toward the moved toward the pendulum bob from the left, pendulum bob from the left, causing the pendulum to causing the pendulum to deflectdeflect


►Draw a free body diagram for the Draw a free body diagram for the pendulum bob; you will know the mass pendulum bob; you will know the mass of the bob and the separation of the two of the bob and the separation of the two spheres and the angle the pendulum spheres and the angle the pendulum support makes with the verticalsupport makes with the vertical

►Develop an equation that will allow you Develop an equation that will allow you to solve for the electrostatic force to solve for the electrostatic force experienced by the pendulum (and the experienced by the pendulum (and the second sphere)second sphere)

Pith BallPith Ball

cos

0

TF

TF

TF

e

xe

xe

sin

0

TF

TF

TF

g

gg

yg

tan

sin

cossin

mgF

mgF

mgT

e

e


Separation (m)Angle

(with vertical)

0.150 11.52319

0.130 15.18589

0.110 20.76193

0.090 29.52358

0.070 43.11136


►What type of relationship does this What type of relationship does this display as the distance between the display as the distance between the point charges is increased or point charges is increased or decreased?decreased?


►Coulomb’s Law is given as:Coulomb’s Law is given as:

221

r

qkqFe

►Electric Force is the force felt by Electric Force is the force felt by separated (positive or negative) separated (positive or negative) charges.charges. Opposite charges attractOpposite charges attract Like charges repelLike charges repel

Electric Force: Coulomb’s Electric Force: Coulomb’s LawLaw

+ -

++

221

r

qkqFe 2

29100.9CNmk


►Positive force will result when:Positive force will result when: Two positively charged particlesTwo positively charged particles Two negatively charged particlesTwo negatively charged particles

►Negative force will result when:Negative force will result when: One positively and negatively charged One positively and negatively charged

particleparticle

►Positive force indicates repulsionPositive force indicates repulsion►Negative force indicates attractionNegative force indicates attraction

221

r

qkqFe

PracticePractice

►What attractive force does an electron What attractive force does an electron in a hydrogen atom experience?in a hydrogen atom experience?

►What attractive force does an electron What attractive force does an electron in helium experience?in helium experience?

Applications of Applications of Coulomb’s LawCoulomb’s Law


Coulomb Sample ProblemCoulomb Sample Problem

►Three charges are arranged in a line; if Three charges are arranged in a line; if the three charges are 15the three charges are 15μμC, -12C, -12μμC and C and 1818μμC respectively. The distance C respectively. The distance between the first two charges is 0.20m between the first two charges is 0.20m and the second and third charges is and the second and third charges is 0.30m. What is the force experienced 0.30m. What is the force experienced by the first charge?by the first charge?

Coulomb Sample ProblemCoulomb Sample Problem

►What What force is experienced by the force is experienced by the remaining two charges?remaining two charges?

Force (Vector) AdditionForce (Vector) Addition

►To add forces, resolve each force into To add forces, resolve each force into its components and treat the forces in its components and treat the forces in the x-direction and y-direction the x-direction and y-direction independentlyindependently

►Once you sum the x and y Once you sum the x and y components, use Pythagorean components, use Pythagorean Theorem and Trigonometry to resolve Theorem and Trigonometry to resolve into a resultant forceinto a resultant force

ExampleExample

►A point P has forces of 12.0N at 24.3A point P has forces of 12.0N at 24.3°, °, 17.6N at 112°, 6.78N at 241° and 17.6N at 112°, 6.78N at 241° and 10.2N at 74.4°.10.2N at 74.4°. Determine the resultant vectorDetermine the resultant vector

►25.5N, 81.4°25.5N, 81.4°

Coulomb’s Law and Vector Coulomb’s Law and Vector AdditionAddition

►When we consider an electrostatic When we consider an electrostatic system, we need to use Coulomb’s system, we need to use Coulomb’s Law to determine the magnitude and Law to determine the magnitude and direction of each forcedirection of each force

►Once the magnitude and direction of Once the magnitude and direction of each force has been determined, then each force has been determined, then the vector sum can be completedthe vector sum can be completed

Coulomb’s Law in 2DCoulomb’s Law in 2D

►Three charges are arranged as follows; Three charges are arranged as follows; a -2.0a -2.0μμC is placed 4.0m due north of a C is placed 4.0m due north of a 3.03.0μμC charge and 3.0m due west of a C charge and 3.0m due west of a 5.05.0μμC charge. What is the force C charge. What is the force experienced by the -2.0experienced by the -2.0μμC charge?C charge?


NxF

r

qkqF

e

e

312

221

12

104.3

-2.0μC

3.0 μ C

5.0 μ C

4.0m

3.0m

NxF

r

qkqF

e

e

323

223

23

104.5

1

2

3


o

oo

233

18053

3.0 μ C2

NxF

NxF

NxF

NxF

NxF

NF

ye

ye

xe

xe

ye

xe

323

323

323

323

312

12

103.4

233sin104.5

102.3

233cos104.5

104.3

0


►Use the x and y component data to Use the x and y component data to determine the resultant force vectordetermine the resultant force vector

NxF

NxNxF

NxF

NxNF

ey

ey

ex

ex

4

33

3

3

100.9

103.4104.3

102.3

102.30

oe

o

e

NxF

NxF

196,103.3

16

103.3

3

3

Electric FieldsElectric Fields


Field TheoryField Theory

►When forces exist without contact, it When forces exist without contact, it can be useful to use field theory to can be useful to use field theory to describe the force experienced by a describe the force experienced by a particle at any point in spaceparticle at any point in space

►We live in a gravitational field where We live in a gravitational field where the separation between massive the separation between massive objects results in attractive forcesobjects results in attractive forces

► In a similar way, we can think of an In a similar way, we can think of an electric fieldelectric field

Electric Field MappingElectric Field Mapping

►To map an electric field, a small To map an electric field, a small positive test charge is placed in the positive test charge is placed in the field and the magnitude and field and the magnitude and direction of the force is recordeddirection of the force is recorded

►The test charge is then moved The test charge is then moved throughout the electric field and a throughout the electric field and a map of the field is createdmap of the field is created

► If the force experienced by the test If the force experienced by the test charge can be measured, then we charge can be measured, then we can map the fieldcan map the field

Test ChargeTest Charge

► The test charge that is used The test charge that is used must be small compared to must be small compared to the charge creating the fieldthe charge creating the field

► If not, the test charge’s field If not, the test charge’s field will change the field that is will change the field that is being investigatedbeing investigated

► The electric field should be The electric field should be the same regardless of the the same regardless of the test charge usedtest charge used

Field Lines – Two Positive Field Lines – Two Positive ChargesCharges

Field Lines – Two Opposing Field Lines – Two Opposing ChargesCharges

ProblemProblem

► What are the What are the relative magnitudes relative magnitudes of the charges in of the charges in the diagram?the diagram?

► What is the polarity What is the polarity of each of the of each of the charges?charges?

Multiple ChargesMultiple Charges

► It is also possible to It is also possible to consider what consider what happens with happens with multiple charges:multiple charges:

Electric Field IntensityElectric Field Intensity

►The electric field can be determined The electric field can be determined using the force experienced by a using the force experienced by a particle and the charge on the particleparticle and the charge on the particle

''

q

FE onq

Electric FieldElectric Field

►The electric field also has a direction; The electric field also has a direction; since the field is the superposition of since the field is the superposition of all the electric field vectors at a given all the electric field vectors at a given point in space where:point in space where:

'1'

1 q

FE onq

iEE

Electric FieldElectric Field

►A charge of 2.0mC is placed at the A charge of 2.0mC is placed at the origin and a charge of -5.0mC is origin and a charge of -5.0mC is placed at the point (3,0); what electric placed at the point (3,0); what electric field exists at:field exists at: (1,0)(1,0) (4,0)(4,0) (-1,0)(-1,0)

►Where is the electric field equal to Where is the electric field equal to zero?zero?

Electric PotentialElectric Potential


Electric Potential EnergyElectric Potential Energy

► Gravitational Gravitational potential energy is potential energy is due to mass, due to mass, gravitational field gravitational field intensity and intensity and separationseparation

► Electric potential Electric potential energy is due to energy is due to charge, electric charge, electric field intensity and field intensity and separationseparation r

kqQE

rr

kqQE

qrq

FE

EqrE

p

p

p

p

2

Potential DifferencePotential Difference►Similar to gravitational potential Similar to gravitational potential

difference, electric potential difference, electric potential difference is measured with respect difference is measured with respect to a reference point (usually the to a reference point (usually the ground) which we call zeroground) which we call zero

►This concept is not as useful for This concept is not as useful for gravitational difference as objects gravitational difference as objects have different masses, but since have different masses, but since each charge carrier has the same each charge carrier has the same charge, this concept has value for charge, this concept has value for electric potential differenceelectric potential difference

Voltage or Potential Voltage or Potential DifferenceDifference

► Electric potential Electric potential difference is known difference is known as voltageas voltage

► One volt is defined One volt is defined as one joule per as one joule per coulombcoulomb

► Electric Potential is Electric Potential is NOTNOT electric electric potential energypotential energy

r

kQV

q

EV p

These plots show the potential due to (a) positive and (b) negative charge.

What minimum work is required by an external force to bring a charge q = 3.00 μC from a great distance away (r = infinity) to a point 0.500 m from a charge Q = 20.0 μC ?

Analogy between gravitational and electrical potential energy:

Both rocks have the samegravitational potential, but the bigger rock has more Ep.

Both charges have thesame electric potential,but the 2Q charge hasmore Ep.

What is the change in potential energy of the electron in going from a to b?What is the speed of the electron as a result of this acceleration?Repeat both calculations for a proton.

Uniform Electric FieldUniform Electric Field

► As previously seen, As previously seen, it is possible to it is possible to produce a uniform produce a uniform electric fieldelectric field

► The intensity of the The intensity of the field is a function of field is a function of the voltage and the voltage and separation of the separation of the platesplates

EdV

Equipotential Lines

•An equipotential (represented by the green dashed lines) is a line or surface over which the potential is constant.

•Electric field lines are perpendicular to equipotentials.

•The surface of a conductor is an equipotential.

Equipotential Lines

The Electron Volt, a Unit of Energy

A Joule is too large when dealing with electrons or atoms, so electron volts are

used. One electron volt (eV) is the energy gained by an electron moving through a

potential difference of one volt.

Elementary ChargeElementary Charge

►Robert Millikan investigated the charge Robert Millikan investigated the charge on an electron in his famous oil-drop on an electron in his famous oil-drop experimentexperiment

►He was awarded the Nobel Prize in He was awarded the Nobel Prize in 1923 for his 1917 research that led to 1923 for his 1917 research that led to the elementary charge of 1.60x10the elementary charge of 1.60x10-19-19CC

►Today, the accepted value of the Today, the accepted value of the elementary charge is 1.60217733x10elementary charge is 1.60217733x10--

1919CC

Elementary ChargeElementary Charge

► Since we know the Since we know the value of the value of the elementary charge, elementary charge, we can determine we can determine the number of the number of charge carriers or charge carriers or the total charge the total charge with the following with the following equationequation

Neq

coulomb’s law physics 12. electroscope ► draw a diagram showing the forces that exist on the...

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