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Coulomb’s Law. Physics 12. Electroscope. Draw a diagram showing the forces that exist on the leaves of the electroscope when it is placed close to the Van de Graff generator. Consider the following pendulum The mass initially shares charge with an identical sphere

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Coulomb s law

Coulomb’s Law

Physics 12


Electroscope
Electroscope

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


Coulomb s pendulum

Consider the following pendulum

The mass initially shares charge with an identical sphere

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

Coulomb’s Pendulum


Coulomb s pendulum1
Coulomb’s Pendulum

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

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




Coulomb s pendulum3
Coulomb’s Pendulum

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


Coulomb s law1
Coulomb’s Law

  • Coulomb’s Law is given as:


Electric force coulomb s law
Electric Force: Coulomb’s Law

  • Electric Force is the force felt by separated (positive or negative) charges.

    • Opposite charges attract

    • Like charges repel

+

-

+

+


Coulomb s law2
Coulomb’s Law

  • Positive force will result when:

    • Two positively charged particles

    • Two negatively charged particles

  • Negative force will result when:

    • One positively and negatively charged particle

  • Positive force indicates repulsion

  • Negative force indicates attraction


Practice
Practice

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

  • What attractive force does an electron in helium experience?



Coulomb sample problem
Coulomb Sample Problem

  • Three charges are arranged in a line; if the three charges are 15μC, -12μC and 18μC respectively. The distance between the first two charges is 0.20m and the second and third charges is 0.30m. What is the force experienced by the first charge?


Coulomb sample problem1
Coulomb Sample Problem

  • What force is experienced by the remaining two charges?


Force vector addition
Force (Vector) Addition

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

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


Example
Example

  • A point P has forces of 12.0N at 24.3°, 17.6N at 112°, 6.78N at 241° and 10.2N at 74.4°.

    • Determine the resultant vector

  • 25.5N, 81.4°


Coulomb s law and vector addition
Coulomb’s Law and Vector Addition

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

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


Coulomb s law in 2d
Coulomb’s Law in 2D

  • Three charges are arranged as follows; a -2.0μC is placed 4.0m due north of a 3.0μC charge and 3.0m due west of a 5.0μC charge. What is the force experienced by the -2.0μC charge?


Coulomb s law in 2d1
Coulomb’s Law in 2D

-2.0μC

5.0 μ C

1

3.0m

3

4.0m

3.0 μ C

2



Coulomb s law in 2d3
Coulomb’s Law in 2D

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


Electric fields

Electric Fields

Physics 12


Field theory
Field Theory

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

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

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


Electric field mapping
Electric Field Mapping

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

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

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


Test charge

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

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

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

Test Charge


Field lines two positive charges
Field Lines – Two Positive Charges charge creating the field


Field lines two opposing charges
Field Lines – Two Opposing Charges charge creating the field


Problem

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

What is the polarity of each of the charges?

Problem



Electric field intensity
Electric Field Intensity charges:

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


Electric field
Electric Field charges:

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


Electric field1
Electric Field charges:

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

    • (1,0)

    • (4,0)

    • (-1,0)

  • Where is the electric field equal to zero?


Electric potential

Electric Potential charges:

Physics 12


Electric potential energy
Electric Potential Energy charges:

  • Gravitational potential energy is due to mass, gravitational field intensity and separation

  • Electric potential energy is due to charge, electric field intensity and separation


Potential difference
Potential Difference charges:

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

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


Voltage or potential difference
Voltage or Potential Difference charges:

  • Electric potential difference is known as voltage

  • One volt is defined as one joule per coulomb

  • Electric Potential is NOT electric potential energy



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 same

gravitational potential, but

the bigger rock has more Ep.

Both charges have the

same electric potential,

but the 2Q charge has

more 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 field

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

The intensity of the field is a function of the voltage and separation of the plates

Uniform Electric Field


Equipotential Lines electric field

  • 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 electric field


The Electron Volt, a Unit of Energy electric field

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 charge
Elementary Charge electric field

  • Robert Millikan investigated the charge on an electron in his famous oil-drop experiment

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

  • Today, the accepted value of the elementary charge is 1.60217733x10-19C


Elementary charge1
Elementary Charge electric field

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


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