General Physics 2 - Electric Charge and Coulomb's Law PDF

General Physics 2 Contents Electric charge Coulomb’s Law Facts on electric charges There are two types of electric charge, called positive and negative. The subatomic particle called a proton has a positive charge, and an electron has a negative charge. Charge comes in quantized units. All...

General Physics 2 Contents Electric charge Coulomb’s Law Facts on electric charges There are two types of electric charge, called positive and negative. The subatomic particle called a proton has a positive charge, and an electron has a negative charge. Charge comes in quantized units. All protons carry the same amount of charge +e, and all electrons carry a charge -e. Like charges repel each other; unlike charges attract. Charge is conserved. The total charge on an object is the sum of all the individual charges (protons and electrons) carried by the object. The total charge can be positive, negative, or zero. Charge can move from place to place but the total charge of the universe does not change. What is electric charge? Charge is a fundamental property of matter: the amount of charge that is “on” or “carried by” a particle determines how the particle reacts to electric and magnetic fields. It is not possible to define the meaning of charge because it is a basic and fundamental term. In the SI system of units, charge is measured in coulombs (C) in honor of French physicist Charles de Coulomb (1736-1806). Charge of electrons and protons Electron charge = −e = −1.60 × 10−19 C (Eq. 1) Proton charge = +e = +1.60 × 10−19 C (Eq. 2) From the above, it can be derived that 1𝐶 = 6.25 × 1018 e. In other words, a charge of -1C requires 6 250 000 000 000 000 000 electrons, or approx. 6 million, million, million electrons. The quantity e is always positive, so when describing the charge of an electron, a negative sign should be affixed to it. Some Notations and Rules e is the amount of charge of proton which is always positive q or Q denote the total charge of an object. They can be positive or negative. When we say that an object has a charge q, it means that the total charge of the particle is q. An object with charge q=0 does not necessarily mean that it have no protons or electrons. It could be that they have equal number of protons and electrons. Coulomb’s Law Consider two charged objects that they can be modeled as point particles. If the charges carried by the two objects are 𝑞1 and 𝑞2 and they are separated by a distance 𝑟, the electric force between the two objects can be written as 𝑞1 𝑞2 𝐹=𝑘 (Eq. 3) 𝑟2 Eq. 3 is called the Coulomb’s Law, where 𝑘 is a constant with value 𝑘 = 8.99 × 109 𝑁 ∙ 𝑚2 /𝐶 2 (Eq. 4) The direction of the Force F is along the line that connects the two charges. Figure 1: Coulomb’s Law Restriction of Coulomb’s Law The objects should be very small, or The size of the objects should be much smaller than their separation r Alternative Formula for Coulomb’s Law: 𝑞1 𝑞2 𝐹= (Eq. 5) 4𝜋𝜀0 𝑟2 where 𝜀0 is called the permittivity of free space, having the value 2 −12 𝐶 𝜀0 = 8.85 × 10 (Eq. 6) 𝑁∙𝑚2 The values of 𝜀0 and 𝑘 are related by 1 =𝑘 4𝜋𝜀0 Activity 1. Answer the following problems in your notebook. 1. Suppose you are given a box holding 1g (0.001 kg) of pure electrons. If two similar boxes are placed 1m apart, find the electric force they exert on each other. (𝑚𝑒 = 9.11 × 10−31 𝑘𝑔) 2. A sack of rice is approximately 50kg. How many sacks of rice is needed so that their weight is equal to the force on problem 1. 3. Compare gravitational force and electric force. Using Coulomb’s Law to Clean the Air 4. Coal burning power plants produce large amounts of potential pollution in the form of small particles (soot). Modern smokestacks use devices called scrubbers to remove these particles from the smoke they emit. Scrubbers use a two-step process: electrons are first added to the soot particle, and an electric force then pulls the particle out of the smoke stream. In this example, we analyze the force on a soot particle after electrons are added. Continuation: Consider a soot particle of mass (𝑚𝑠𝑜𝑜𝑡 = 1.0 𝑛𝑎𝑛𝑜𝑔𝑟𝑎𝑚 = 1.0 × 10−9 𝑔 = 1.0 × 10−12 𝑘𝑔), which corresponds to a diameter of a few microns. Some number of electrons have been added to give the particle a total charge 𝑞𝑠𝑜𝑜𝑡. Suppose the collector has a total charge 𝑞𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑜𝑟 = 1.0 × 10−6 𝐶 and is small enough to be treated as a point charge at the rim of the smokestack. (a) If the separation between the collector and the soot particle is 𝑟 = 0.10𝑚, what is the value of 𝑞𝑠𝑜𝑜𝑡 so that the electric force exerted on the particle is equal to its weight? (b) How many electrons must be added to the soot particle? Answers to activity 1 1. 𝐹 = 3 × 1026 𝑁 2. 6 × 1026 sacks of rice 3. The gravitational force is always attractive, while the electric force can be attractive or repulsive depending whether the charges have different or same charge respectively. It can also be said or argued that electric forces are stronger than gravitational force. Example of this is problem no. 1. 4. (a) 𝑞𝑠𝑜𝑜𝑡 = 1.1 × 10−17 𝐶 (b) 69 electrons Generalization References Book: Giordano, Nicholas. General Physics 2. Manila: Rex Book Store, Inc, 2018. (Philippine Edition, Adapted from Cengage Learning Asia Pte Ltd) Image (Figure 1): https://www.google.com/search?q=coulomb%27s+law+illustration&client=o pera&hs=opY&tbm=isch&source=iu&ictx=1&fir=NHrVKlMzBR- 2fM%253A%252Cld59U8E10Lj4AM%252C_&usg=AI4_- kQdwD1SKLg8G7M0KT6s95h- 4aDQsA&sa=X&ved=2ahUKEwjtjNbbw8zeAhUEgbwKHfJIAfwQ9QEwDHoECA MQBg#imgrc=NHrVKlMzBR-2fM: (Retrived: November 11, 2018)