1 Norah Ali Al-moneef king Saud unversity 23.1 Properties of Electric Charges 23.2 Charging Objects By Induction 23.3 Coulomb’s Law 23.4 The Electric Field 23.6 Electric Field Lines 23.7 Motion of Charged Particles in a Uniform Electric Field 1/10/2006

Electric Charge Types: – 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 2 Norah Ali Al-moneef king Saud unversity 1/10/2006

Charge in the Atom Protons (+) Electrons (-) Ions Polar Molecules 3 Norah Ali Al-moneef king Saud unversity 1/10/2006

23.1 Properties of Electric Charges Conservation electricity is the implication that electric charge is always conserved. That is, when one object is rubbed against another, charge is not created in the process. The electrified state is due to a transfer of charge from one object to the other. One object gains some amount of negative charge while the other gains an equal amount of positive charge. Quantization – The smallest unit of charge is that on an electron or proton. (e = 1.6 x C) It is impossible to have less charge than this It is possible to have integer multiples of this charge 4 Norah Ali Al-moneef king Saud unversity 1/10/2006

Conductors and Insulators Conductor transfers charge on contact Insulator does not transfer charge on contact Semiconductor might transfer charge on contact 5 Norah Ali Al-moneef king Saud unversity 23.2 Charging Objects By Induction 1/10/2006

Charge Transfer Processes Conduction Polarization Induction 6 Norah Ali Al-moneef king Saud unversity 1/10/2006

23-3 Coulomb’s Law Empirical Observations Formal Statement Direction of the force is along the line joining the two charges 7 Norah Ali Al-moneef king Saud unversity 1/10/2006

Norah Ali Al-moneef king Saud unversity 8 Consider two electric charges: q 1 and q 2 The electric force F between these two charges separated by a distance r is given by Coulomb’s Law The constant k is called Coulomb’s constant and is given by The coulomb constant is also written as  0 is the “electric permittivity of vacuum” – A fundamental constant of nature 1/10/2006

Norah Ali Al-moneef king Saud unversity 9 Double one of the charges – force doubles Change sign of one of the charges – force changes direction Change sign of both charges – force stays the same Double the distance between charges – force four times weaker Double both charges – force four times stronger 1/10/2006

Norah Ali Al-moneef king Saud unversity 10 Example: What is the force between two charges of 1 C separated by 1 meter? Answer: 8.99 x 10 9 N, 1/10/2006

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 m The magnitude of the Coulomb force is F = kQ 1 Q 2 /r 2 = (9.0 x 10 9 N · m 2 /C 2 )(26)(1.60 x 10 –19 C)(1.60 x 10 –19 C)/(1.5x10 –12 m) 2 = 2.7 x 10 –3 N. 11 Norah Ali Al-moneef king Saud unversity 1/10/2006

Norah Ali Al-moneef king Saud unversity 12 Example - The Helium Nucleus Part 1: The nucleus of a helium atom has two protons and two neutrons. What is the magnitude of the electric force between the two protons in the helium nucleus? Answer: 58 N Part 2: What if the distance is doubled; how will the force change? Answer: 14.5 N Inverse square law: If the distance is doubled then the force is reduced by a factor of 4. 1/10/2006

13 Consider two charges located on the x axis The charges are described by – q 1 = 0.15  Cx = 0.0 m – q 2 = 0.35  Cx = 0.40 m Where do we need to put a third charge for that charge to be at an equilibrium point? At the equilibrium point, the forces from the two charges will cancel. Example - Equilibrium Position Norah Ali Al-moneef king Saud unversity 1/10/2006 Here the forces from q 1 and q 2 can balance. q3q3

Zero Resultant Force, Example – 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 Two fixed charges, 1mC and -3mC are separated by 10cm as shown in the figure (a) where may a third charge be located so that no force acts on it? 1/10/ Norah Ali Al-moneef king Saud unversity

1/10/2006 Norah Ali Al-moneef king Saud unversity 15 two charges are located on the positive x-axis of a coordinate system, as shown in the figure. Charge q 1 =2nC is 2cm from the origin, and charge q 2 =-3nC is 4cm from the origin. What is the total force exerted by these two charges on a charge q 3 =5nC located at the origin? The total force on q 3 is the vector sum of the forces due to q 1 and q 2 individually. The total force is directed to the left, with magnitude 1.41x10 -4 N. Example:

Norah Ali Al-moneef king Saud unversity 16 Example - Charged Pendulums Consider two identical charged balls hanging from the ceiling by strings of equal length 1.5 m (in equilibrium). Each ball has a charge of 25  C. The balls hang at an angle  = 25  with respect to the vertical. What is the mass of the balls? Step 1: Three forces act on each ball: Coulomb force, gravity and the tension of the string. x y 1/10/2006

Norah Ali Al-moneef king Saud unversity 17 Example - Charged Pendulums (2) Step 2: The balls are in equilibrium positions. That means the sum of all forces acting on the ball is zero! Answer: m = 0.76 kg A similar analysis applies to the ball on the right. d=2 l sin  1/10/2006

Norah Ali Al-moneef king Saud unversity 18 Electric Force and Gravitational Force Coulomb’s Law that describes the electric force and Newton’s gravitational law have a similar functional form Both forces vary as the inverse square of the distance between the objects. Gravitation is always attractive. k and G give the strength of the force. 1/10/2006

Norah Ali Al-moneef king Saud unversity 19 Example: An electron is released above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel out the gravitational force on it. How far below the first electron is the second? e e mg FeFe r = ? 5.1 m 1/10/2006

Compare the electrostatic and gravitational the forces F e /F g = 2 x  The force of gravity is much weaker than the electrostatic force The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.3 x m. Find the magnitudes of the electric force and the gravitational force between the two particles. 1/10/ Norah Ali Al-moneef king Saud unversity

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Electric Forces and Vectors Electric Fields and Forces are ALL vectors, thus all rules applying to vectors must be followed. Consider three point charges, q 1 = 6.00 x10 -9 C (located at the origin),q 3 = 5.00x10 -9 C, and q 2 = -2.00x10 -9 C, located at the corners of a RIGHT triangle. q 2 is located at y= 3 m while q 3 is located 4m to the right of q 2. Find the resultant force on q 3. q1 q2q3 3m 4m 5m q3 Which way does q 2 push q 3 ? Which way does q 1 push q 3 ? F on 3 due to 2 F on 3 due to 1   = 37  = tan -1 (3/4) 1/10/ Norah Ali Al-moneef king Saud unversity

q1q1 q2q2 q3q3 3m 4m 5m q3q3 F on 3 due to 2 F on 3 due to 1   = 37  = tan -1 (3/4) 5.6 x10 -9 N 1.1x10 -8 N F 3,1 cos37 F 3,1 sin x10 -9 N above the +x 1/10/ Norah Ali Al-moneef king Saud unversity

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? 24 Norah Ali Al-moneef king Saud unversity We find the magnitudes of the individual forces on the charge at the upper right corner: F 1 = F 2 = kQQ/L 2 = kQ 2 /L 2 = (9 x10 9 N · m 2 /C 2 )(6 x10 –3 C) 2 /(0.100 m) 2 = 3.24 x10 7 N. F 3 = kQQ/(L√2)2 = kQ2/2L2 = (9 x10 9 N · m 2 /C 2 )(6 x10 –3 C) 2 /2(0.100 m) 2 = 1.62 x10 7 N. 1/10/2006

Norah Ali Al-moneef king Saud unversity 25 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 ء 10 7 N away from the center of the square.. 1/10/2006

Norah Ali Al-moneef king Saud unversity 26 Example - Four Charges Consider four charges placed at the corners of a square with sides of length 1.25 m as shown on the right. What is the magnitude of the electric force on q 4 resulting from the electric force from the remaining three charges? Answer: F ( on q 4 ) = N … and the direction? 1/10/2006

23-7; Three point charges are located at the corners of an equilateral triangle. Calculate the net electric force on the 7.00 uC charge. HOMEWORK : 23-8: Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal insulating rod extending from the origin to the point x =d. a third small charged bead is free to slide on the rod. At what position is the third bead in equilibrium? Can it be in stable equilibrium? 1/10/ Norah Ali Al-moneef king Saud unversity

23-12; An object having a net charge of 24.0 C is placed in a uniform electric field of 610 N/C that is directed vertically. What is the mass of this object if it “floats” in the field? 3-18; Two 2.00uC point charges are located on the x axis. One is at x = 1.00 m, and the other is at x = m. (a) Determine the electric field on the y axis at y =0.500 m. (b) Calculate the electric force on a uC charge placed on the y axis at y = m ; An electron and a proton are each placed at rest in an electric field of 520 N/C. Calculate the speed of each particle 48.0 ns after being released ; The electrons in a particle beam each have a kinetic energy of 1.60 x J. What are the magnitude and direction of the electric field that stops these electrons in a distance of 10.0 cm? 1/10/ Norah Ali Al-moneef king Saud unversity