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# Coulomb’s Law - PowerPoint PPT Presentation

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

Physics 12

• 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

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

• 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)

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

• Coulomb’s Law is given as:

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

• Opposite charges attract

• Like charges repel

+

-

+

+

• 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

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

• What attractive force does an electron in helium experience?

### Applications of Coulomb’s Law

Physics 12

• 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?

• What force is experienced by the remaining two charges?

• 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

• 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°

• 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

• 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?

-2.0μC

5.0 μ C

1

3.0m

3

4.0m

3.0 μ C

2

3.0 μ C

2

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

### Electric Fields

Physics 12

• 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

• 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

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 charge creating the field

Field Lines – Two Opposing Charges charge creating the field

What is the polarity of each of the charges?

Problem

Multiple Charges

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 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 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 charges:

Physics 12

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 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 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 ?

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.

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 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 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