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

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 ► 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)

Pith Ball

Coulomb’s Pendulum Separation (m) Angle (with vertical)

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

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

► Electric Force is the force felt by separated (positive or negative) charges.  Opposite charges attract  Like charges repel Electric Force: Coulomb’s Law +- ++

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 ► 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

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

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 ► 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 ► 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 ► 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 2D -2.0μC 3.0 μ C 5.0 μ C 4.0m 3.0m1 2 3

Coulomb’s Law in 2D 3.0 μ C 2

Coulomb’s Law in 2D ► Use the x and y component data to determine the resultant force vector

Electric Fields Physics 12

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 ► 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

Field Lines – Two Positive Charges

Field Lines – Two Opposing Charges

Problem ► What are the relative magnitudes of the charges in the diagram? ► What is the polarity of each of the charges?

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

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

Electric Field ► 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 ► 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 Physics 12

Electric Potential Energy ► 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 ► 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 ► Electric potential difference is known as voltage ► One volt is defined as one joule per coulomb ► Electric Potential is NOT electric potential energy

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 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

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 Charge ► 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 1.60x C ► Today, the accepted value of the elementary charge is x C

Elementary Charge ► 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