University Physics: Waves and Electricity Lecture 6 Ch21. Coulomb’s Law University Physics: Waves and Electricity Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com 2016

Homework 5: Ambulance Siren An ambulance with a siren emitting a whine at 1600 Hz overtakes and passes a cyclist pedaling a bike at 8 m/s. After being passed, the cyclist hears a frequency of 1590 Hz. (a) How fast is the ambulance moving? (b) What frequency did the cyclist hear before being overtaken by the ambulance?

Solution of Homework 5: Ambulance Siren

Electric Charge Static cling, an electrical phenomenon that accompanies dry weather, causes the pieces of paper to stick to one another. This is an example that reveals the existence of electric charge. In fact, every object contains a vast amount of electric charge. Electric charge is an intrinsic characteristic of the fundamental particles making up those objects. The vast amount of charge in an everyday object is usually hidden because the object contains equal amounts of the two kinds of charge: positive charge and negative charge. With such a balance of charge, the object is said to be electrically neutral (contains no net charge). If the two types of charge are not in balance, we say that an object is charged, it has a net charge.

Electric Charge Charged objects interact by exerting forces on one another. Charges with the same electrical sign repel each other, while charge with opposite electrical signs attract each other. This rule will be described quantitatively as Coulomb’s law of electrostatic force between charges. (The term electrostatic is used to emphasize that the charges are stationary relative to each other.)

Coulomb’s Law If two charged particles are brought near each other, they each exert a force on the other. If the particles have the same sign of charge, they repel each other.  The force on each particle is directed away from the other particle. If the particles have opposite signs of charge, they attract each other.  The force on each particle is directed toward the other particle.

Coulomb’s Law This force of repulsion or attraction due to the charge properties of objects is called an electrostatic force. The equation giving the force for charged particles is called Coulomb’s law, named after Charles-Augustin de Coulomb, who did the experiments in 1785. If particle 1 has charge q1 and particle 2 has charge q2, the force on particle 2 is: The term is a unit vector to the direction from position of q1 to position of q2. The term k is a constant.

Coulomb’s Law ε0 is a constant denoted as permittivity in vacuum, a measure of how the vacuum medium is affected by an electric field. As can be deducted from the constants, the SI unit of charge is the coulomb (C). x y q1 + r12 → r1 → q2 r2 → + F2 →

Some Examples on Vectors Example: If , find and . Example: If and , find and . Both vectors are of opposite direction, but have the same magnitude

Coulomb’s Law If we have n charged particles, they interact independently in pairs, and the force on any one of them, is given by the vector sum. Let us say, we have n particles, then the force on particle 1 is given by: x y q1 + q2 F21 → + q3 F23 → F2,net → –

Example 1: Coulomb’s Law The figure below shows two positively charged particles fixed in place on an x axis. The charges are q1 = 1.610–19 C and q2 = 3.210–19 C. The q1 is located on the origin, while the separation is R = 0.02 m. What are the magnitude and direction of the electrostatic force F12 on particle 1 from particle 2? →

Example 2: Coulomb’s Law Now, particle 3 lies on the x axis between particles 1 and 2. Particle 3 has charge q3 = –3.210–19 C and is at a distance 3/4R from particle 1. What is the net electrostatic force F1,net on particle 1 due to particles 2 and 3? →

Example 3: Coulomb’s Law Particle 3 from previous example is now replaced by particle 4. Particle 4 has charge q4 = –3.210–19 C, is at a distance 3/4R from particle 1, and lies on a line that makes an angle θ = 60° with the x axis. What is the net electrostatic force F1,net on particle 1 due to particles 2 and 4? →

Example 3: Coulomb’s Law

Checkpoint a, c, b Less than 45° The figure below shows three arrangements of one electron (e) and two protons (p). (a) Rank the arrangements according to the magnitude of the net electrostatic force on the electron due to the protons, largest first (b) In situation c, is the angle between the net force on the electron and the line labeled d less than or more than 45 °? a, c, b Less than 45°

Example 4: Coulomb’s Law Two particles are fixed in place: a particle of charge q1 = +8q at the origin and a particle of charge q2 = –2q at x = L. At what point can a particle of charge q3 = +4q be placed so that it is in equilibrium (the net force on q3 is zero)? F32 → F31 → F32 → : impossible to place q3 on the left of q1 or in the middle between q1 and q2 F31 → F32 → : the only possibility is to place q3 to the right-hand side of q2 F31 →

Example 4: Coulomb’s Law q3 between q1 and q2 q3 to the right of q2 Charge q3 must be placed on the x axis, at distance L to the right of q3, or, at point (2L,0) F32 → F31 → L x

Charge Is Quantized Experiment shows that electric charge is not continuous but is made up of multiples of a certain elementary charge (quantized). Any positive or negative charge q that can be detected can be written as in which e, the elementary charge, has the approximate value The elementary charge e is one of the important constants of nature. The electron and proton both have a charge of magnitude e.

Exercise Problems Three point charges are arranged along the x- axis. Charge q1 = +3 μC is at the origin, and the charge q2 = –5 μC is at x = 0.2 m. Charge q3 = –8 μC. Where is q3 located if the net force on q1 is 7 N in the negative x-direction? Answer: x = –0.144 m. Two point charges are located on an xy-plane as follows. The first charge, q1 = 2 μC is located at (2,4). The second charge, q2 = –3 μC is located at (1,6). Determine the force vector acting on q2, i.e. F21. → Answer: F21 = 4.824 i – 9.649 j mN ^ →