My Chapter 16 Lecture Outline

Chapter 16: Electric Forces and Fields Electric Charge Conductors & Insulators Coulomb’s Law Electric Field Motion of a Point Charge in a Uniform E-field Conductors in Electrostatic Equilibrium Gauss’s Law (not taught !!)

§16.1 Electric Charge There are two kinds of electric charge: positive and negative. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Questions 1, 2, and 3. A body is electrically neutral if the sum of all the charges in a body is zero. Charge is a conserved quantity.

The elementary unit of charge is e = 1.60210-19 C. The charge on the electron is 1e. The charge on the proton is +1e. The charge on the neutron is 0e. Experiments show that likes charges will repel each other and unlike charges will attract each other and that the force decreases with increasing distance between charges.

+  This body is electrically neutral. An object can become polarized if the charges within it can be separated. When grounded, the sphere will be charged by induction. +  By holding a charged rod near the body, it can be polarized. +

Example (text problem 16. 4): A metallic sphere has a charge of +4 Example (text problem 16.4): A metallic sphere has a charge of +4.0 nC. A negatively charged rod has a charge of 6.0 nC. When the rod touches the sphere, 8.2109 electrons are transferred. What are the charges of the sphere and the rod now? Each electron has a charge 1.60210-19 C so the total charge transferred is 1.3 nC. The rod is left with 6.0 nC + 1.3 nC = 4.7 nC of charge and the sphere now has +4.0 nC  1.3 nC = +2.7 nC of charge.

§16.2 Conductors and Insulators A conductor is made of material that allows electric charge to move through it easily. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 4. An insulator is made of material that does not allow electric charge to move through it easily.

§16.3 Coulomb’s Law The magnitude of the force between two point charges is: where q1 and q2 are the charges, r is the separation between the two charges and k = 8.99109 Nm2/C2. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Questions 5, 6, 7, 8, and 9. and 0 is called the permittivity of free space.

The electric force is directed between the centers of the two point charges. q1 q2 F21 F12 Attractive force between q1 and q2. r q1 q2 F21 F12 Repulsive force between q1 and q2. The electric force is an example of a long-range or field force, just like the force of gravity.

Example: What is the net force on the charge q1 due to the other two charges? q1 = +1.2 C, q2 = 0.60 C, and q3 = +0.20 C. F31 F21  The net force on q1 is Fnet = F21 + F31

The magnitudes of the forces are: Example continued: The magnitudes of the forces are:

The components of the net force are: Example continued: The components of the net force are: Where from the figure

The magnitude of the net force is: Example continued: The magnitude of the net force is: The direction of the net force is:

§16.4 The Electric Field Recall : Where g is the strength of the gravitational field. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Questions 10, 11, 12, 13, 16, and 18. Similarly for electric forces we can define the strength of the electric field E.

For a point charge of charge Q, the magnitude of the force per unit charge at a distance r (the electric field) is: The electric field at a point in space is found by adding all of the electric fields present. Be careful! The electric field is a vector!

Example: Find the electric field at the point P. q1 = +e x = 0 m q2 = 2e x = 1 m P x = 2 m x E is a vector. What is its direction? Place a positive test charge at the point of interest. The direction of the electric field at the location of the test charge is the same as the direction of the force on the test charge.

Locate the positive test charge here. Example continued: q1 = +e q2 = 2e P x Locate the positive test charge here. P q1 = +e q2 = 2e x Direction of E due to charge 1 Direction of E due to charge 2

The net electric field at point P is: Example continued: The net electric field at point P is: The magnitude of the electric field is:

The net E-field is directed to the left. Example continued: The net E-field is directed to the left.

Electric field lines Electric field lines are a useful way to indicate what the magnitude and direction of an electric field is in space. Rules: The direction of the E-field is tangent to the field lines at every point in space. The field is strong where there are many field lines and weak where there are few lines. The field lines start on + charges and end on  charges. Field lines do not cross.

Pictorial representation of the rules on the previous slide:

§16.5 Motion of a Point Charge in a Uniform E-Field Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 14. A region of space with a uniform electric field containing a particle of charge q (q > 0) and mass m.

Apply Newton’s 2nd Law and solve for the acceleration. Fe x y FBD for the charge q Apply Newton’s 2nd Law and solve for the acceleration. One could now use the kinematic equations to solve for distance traveled in a time interval, the velocity at the end of a time interval, etc.

Example: What electric field strength is needed to keep an electron suspended in the air? y Fe w FBD for the electron: To get an upward force on the electron, the electric field must be directed toward the Earth.

Example continued: Apply Newton’s 2nd Law:

§16.6 Conductors in Electrostatic Equilibrium Conductors are easily polarized. These materials have free electrons that are free to move around inside the material. Could incorporate personal response system questions from the College Physics by G/R/R 2E ARIS site (www.mhhe.com/grr), Instructor Resources: CPS by eInstruction, Chapter 16, Question 15. Any charges that are placed on a conductor will arrange themselves in a stable distribution. This stable situation is called electrostatic equilibrium.

When a conductor is in electrostatic equilibrium, the E-field inside it is zero. Any net charge must reside on the surface of a conductor in electrostatic equilibrium.

Just outside the surface of a conductor in electrostatic equilibrium the electric field must be perpendicular to the surface. If this were not true, then any surface charge would have a net force acting on it, and the conductor would not be in electrostatic equilibrium.

Any excess charge on the surface of a conductor will accumulate where the surface is highly curved (i.e. a sharp point).

Summary You need to remember: Properties of Conductors/Insulators Charge Induction Coulomb’s Law The Electric Field Motion of a Point Charge in an Electric Field