Chapter 21 Electric Charge and Electric Fields What is a field? Why have them? What causes fields? Field Type Caused By gravity mass electric charge magnetic moving charge

Electric Charge Types: Arbitrary choice Positive Glass rubbed with silk Missing electrons Negative Rubber/Plastic rubbed with fur Extra electrons Arbitrary choice convention attributed to ? Units: amount of charge is measured in [Coulombs] Empirical Observations: Like charges repel Unlike charges attract

Charge in the Atom Protons (+) Electrons (-) Ions Polar Molecules

Charge Properties Conservation Quantization Charge is not created or destroyed, only transferred. The net amount of electric charge produced in any process is zero. Quantization The smallest unit of charge is that on an electron or proton. (e = 1.6 x 10-19 C) It is impossible to have less charge than this It is possible to have integer multiples of this charge

Conductors and Insulators Conductor transfers charge on contact Insulator does not transfer charge on contact Semiconductor might transfer charge on contact

Charge Transfer Processes Conduction Polarization Induction

The Electroscope

Coulomb’s Law Empirical Observations Formal Statement Direction of the force is along the line joining the two charges

Active Figure 23.7 (SLIDESHOW MODE ONLY)

Coulomb’s Law Example What is the magnitude of the electric force of attraction between an iron nucleus (q=+26e) and its innermost electron if the distance between them is 1.5 x 10-12 m 3.The magnitude of the Coulomb force is F = kQ1Q2/r2 = (9.0 ´ 109 N · m2/C2)(26)(1.60 ´ 10–19 C)(1.60 ´ 10–19 C)/(1.5 ´ 10–12 m)2 = 2.7 ´ 10–3 N.

Hydrogen Atom Example The electrical force between the electron and proton is found from Coulomb’s law Fe = keq1q2 / r2 = 8.2 x 108 N This can be compared to the gravitational force between the electron and the proton Fg = Gmemp / r2 = 3.6 x 10-47 N

Subscript Convention +q1 +q2

More Coulomb’s Law +q1 +q2 Coulomb’s constant: permittivity of free space: Charge polarity: Same sign Force is right Opposite sign Force is Left Electrostatics --- Charges must be at rest!

Superposition of Forces +Q1 +Q2 +Q0 +Q3

Coulomb’s Law Example Q = 6.0 mC L = 0.10 m What is the magnitude and direction of the net force on one of the charges? We find the magnitudes of the individual forces on the charge at the upper right corner: F1= F2 = kQQ/L2 = kQ2/L2 = (9.0 ´ 109 N · m2/C2)(6.00 ´ 10–3 C)2/(0.100 m)2 = 3.24 ´ 107 N. F3= kQQ/(L√2)2 = kQ2/2L2 = (9.0 ´ 109 N · m2/C2)(6.00 ´ 10–3 C)2/2(0.100 m)2 = 1.62 ´ 107 N. The directions of the forces are determined from the signs of the charges and are indicated on the diagram. For the forces on the upper-right charge, we see that the net force will be along the diagonal. For the net force, we have F = F1 cos 45° + F2 cos 45° + F3 = 2(3.24 ´ 107 N) cos 45° + 1.62 ´ 107 N = 6.20 ´ 107 N along the diagonal, or away from the center of the square. From the symmetry, each of the other forces will have the same magnitude and a direction away from the center: The net force on each charge is 6.20 ´ 107 N away from the center of the square. Note that the sum for the three charges is zero.

Zero Resultant Force, Example q1 = 15.0 mC Where is the resultant force equal to zero? The magnitudes of the individual forces will be equal Directions will be opposite Will result in a quadratic Choose the root that gives the forces in opposite directions q2 = 6.0 mC

Electrical Force with Other Forces, Example The spheres are in equilibrium Since they are separated, they exert a repulsive force on each other Charges are like charges Proceed as usual with equilibrium problems, noting one force is an electrical force

Electrical Force with Other Forces, Example cont. The free body diagram includes the components of the tension, the electrical force, and the weight Solve for |q| You cannot determine the sign of q, only that they both have same sign

The Electric Field Charge particles create forces on each other without ever coming into contact. “action at a distance” A charge creates in space the ability to exert a force on a second very small charge. This ability exists even if the second charge is not present. We call this ability to exert a force at a distance a “field” In general, a field is defined: The Electric Field is then: Why in the limit?

Electric Field near a Point Charge +Q -Q Electric Field Vectors Electric Field Lines

Active Figure 23.13 (SLIDESHOW MODE ONLY)

Rules for Drawing Field Lines The electric field, , is tangent to the field lines. The number of lines leaving/entering a charge is proportional to the charge. The number of lines passing through a unit area normal to the lines is proportional to the strength of the field in that region. Field lines must begin on positive charges (or from infinity) and end on negative charges (or at infinity). The test charge is positive by convention. No two field lines can cross.

Electric Field Lines, General The density of lines through surface A is greater than through surface B The magnitude of the electric field is greater on surface A than B The lines at different locations point in different directions This indicates the field is non-uniform

Example Field Lines Line Charge Dipole For a continuous linear charge distribution, Linear Charge Density:

Active Figure 23.24 (SLIDESHOW MODE ONLY)

More Field Lines Surface Charge Density: Volume Charge Density:

Superposition of Fields +q1 +q2 P +q3

Superposition Example Find the electric field due to q1, E1 Find the electric field due to q2, E2 E = E1 + E2 Remember, the fields add as vectors The direction of the individual fields is the direction of the force on a positive test charge

Electric Field of a Dipole y -q +q

Example Three point charges are arranged as shown in Figure P23.19. Find the vector electric field that the 6.00-nC and –3.00-nC charges together create at the origin. (b) Find the vector force on the 5.00-nC charge. Figure P23.19

Example Three point charges are aligned along the x axis as shown in Figure P23.52. Find the electric field at the position (2.00, 0) and the position (0, 2.00). Figure P23.52

FIG. P23.52(a) in +x direction.

P23.19 (a) (b)

Motion of Charged Particles in a Uniform Electric Field -Q +Q

Example A proton accelerates from rest in a uniform electric field of 500 N/C. At some time later, its speed is 2.50 x 106 m/s. Find the acceleration of the proton. How long does it take for the proton to reach this speed? How far has it moved in this time? What is the kinetic energy? e -Q +Q

Motion of Charged Particles in a Uniform Electric Field +Q -e -Q

Active Figure 23.26 (SLIDESHOW MODE ONLY)

Motion of Charged Particles in a Uniform Electric Field -Q +Q Phosphor Screen This device is known as a cathode ray tube (CRT)

Dipoles The combination of two equal charges of opposite sign, +q and –q, separated by a distance l -q +q

Dipoles in a Uniform Electric Field +q -q

Work Rotating a Dipole in an Uniform Electric Field +q -q