The references:

Coulomb's Law In his experiments with charged conducting spheres, Coulomb was able to argue that the force one tiny charged object exerted on a second tiny charged object was directly proportional to the charge on each of them. These tiny objects would ideally be referred to as point charges, idealized point particles with no spatial extent. If the charge on one of the objects doubled, then the force between the objects also doubled. If the charge on both of the objects doubled, then the force between them was four times as much. These force effects hold if the distance between the objects is held constant. These observations show that the force between two charged objects (F) is directly proportional to the product of the charges of the objects (g492): Fag,q In his experiments, Coulomb was also able to show that if the distance between the charged objects doubled, the force fell to one-fourth of its original value. This shows that the force between the charged objects (F) was inversely proportional to the distance between the objects squared (r%): Fo i 2 r By combining these two findings, it is possible to state that f 449, 2 This proportion can be written as a mathematical equation by using a constant: fr = k'fz. r2 In order to assign a numerical value to this constant, it is necessary to know that the standard unit of charge in the Sl system is the coulomb (C) in honour of Charles Coulomb. The precise definition of the coulomb is given in terms of electric current and magnetic field. The constant, k, in this equation is often referred to as Coulomb's law constant. In the S| system, it has the value k = 8.99x10N-m?%/C2 or k = 9.0x10N-m?2/C?2 Coulomb's Law is also sometimes written as F' = - 499 . The quantity &, is called the permittivity of free space. It is not necessary to understand the n 4ne, r meaning of this quantity at this point, but the ratio has the same value as Coulomb's law constant, that is k = 8.99x10N-m2/C2. 4ne o Coulomb's Law can be summarized as follows: The magnitude, F of the electrostatic force exerted by one point charge on another point charge is directly proportional to the magnitudes g4 and g, of the charges and inversely proportional to the square of the distance r between them: f = k'h_?z where k is a proportionality constant whose Sl unit is k = 8.99x10N-m2/C2. ) The electrostatic force is directed along the line joining the charges, and it is attractive if the charges have unlike signs and repulsive if the charges have like signs. ;;' Defining Electric Charge If we use the value of the Coulomb's law constant as stated above, then one way to define the amount of charge contained in a coulomb of charge is to substitute into the Coulomb's Law equation the following numbers. 1.0C 1.0C) =899% 10 N (Lom) Thus, 1 C is that amount of charge that will produce a force of 8.99 x 109 N between two objects placed 1.0 m apart. F= (8.99x109N- mZ/cz) When you rub ordinary objects such as a comb or a plastic ruler, the charge produced is typically a microcoulomb (1 uC = 108 C) or less. Large charges closer to the size of a coulomb can be found in nature in lightning bolts where as much as 25 coulombs can be transferred between the cloud and the ground. The charge on an elementary charge is e = 1.602 x 10719 C. The number of elementary charges found in one coulomb, is 1C = (.24 x 10* elementary charges. 1.602x107"'C/elementary charge ? Magnitude and Direction of the Force When Coulomb's law is written in the form f = kq'# , the magnitude of the force can be found when the magnitudes of the two charges are given. The direction of the force is the line joining the two forces. If the two charges have the same sign, the force on one of the objects is directed away from the other object. Fia + + F; 4O0 1 20p Fy; = force on 1 due to 2 F>; = force on 2 due to 1 If the two objects have opposite charges, the force on one is directed towards the other. + Fy, F - If the signs of the charges are included, then the force will be negative for attraction and positive for repulsion. Notice in the diagrams above that the force one charge exerts on the second is equal but opposite to that exerted by the second on the first. This is in accord with Newton's third law. One method to solve problems involving Coulomb's Law is to ignore the sign of the charges while using the equation, and then to assign the direction of the force after the calculation is performed. This helps to eliminate confusion over what the negative and plus signs for the force mean if the sign of the charges is included in the equation. As an example, suppose that g4 has a value of 2.0 C and g, found to the right of g4 has a value of -4.0 C. Also, suppose that the two charges are separated by a distance of 5.0 m. The force that g, exerts on g is (2.0C)(4.0C) A -288x 10N=2.9x10N 3 = F:(8.99x10N~ ml/cz) The charge g, is a negative charge so it attracts g4 which is a positive charge. This means that the direction of the force on g4 is to the right. :=20C g:=-40C p /7 Comparing the Gravitational Force and the Electric Force The form of Coulomb's Law ' k&qi is remarkably similar to Newton's Law of gravitation g = G M In both cases, the force depends on the inverse 2 2 r 1 square of the distance between the two objects and is directed along the line between them. In addition, the force is proportional to the product of an intrinsic 2 property of each of the two objects, the magnitudes of the charges g4 and g, in Coulomb's law and the masses m, and m, in the gravitation law. But there is also a major difference between the two laws. The electrostatic force can be repulsive or attractive, depending on whether or not the charges have the same sign. The gravitational force however is always an attractive force. jSummary n this lesson, you were introduced to Coulomb's Law describing the forces between charged particles. do0int charges are idealized point particles with no spatial extent. >oulomb's Law states that the magnitude, F of the electrostatic force exerted by one point charge on another point charge is directly proportional to the nagnitudes g4 and g, of the charges and inversely proportional to the square of the distance r between them: f = kql_f where Kk is a proportionality constant 72 vhose Sl unit is k = 8.99x10N-m?%/C2, The electrostatic force is directed along the line joining the charges, and it is attractive if the charges have unlike signs and epulsive if the charges have like signs. Vhen you rub ordinary objects, the charge produced is typically a microcoulomb (1 pC = 106 C) or less. In nature, large charges closer to the size of a coulomb :an be found in lightning bolts where as much as 25 coulombs can be transferred between the cloud and the ground. "he magnitude of the charge found on an electron or a proton is measured to be 1.602 x 10-1 C. This charge is referred to as an elementary charge and is vritten as e = 1.602 x 1071 C. Ve can determine the number of elementary charges found in one coulomb. 1C m = 6.24 x 10' elementary charges Vhen Coulomb's law is written in the form f = kql_?z , the magnitude of the force can be found when the magnitudes of the two charges are given. The lirection of the force is the line joining the two forces. If the two charges have the same sign, the force on one of the objects is directed away from the other object. f the two objects have opposite charges, the force on one is directed towards the other. Joulomb's Law F = k% and Newton's Law of gravitation f GM are very similar. In both cases, the force depends on the inverse square L of the 2 2 2 r r r listance between the two objects and is directed along the line between them. In addition, the force is proportional to the product of the magnitudes of the charges 14 and g in Coulomb's law and the masses my and ms in the gravitation law. However, the electrostatic force can be repulsive or attractive, whereas the jravitational force however is always an attractive force. Question(s): The physics of the DNA molecule. The two strands of the DNA molecule are held together by electrostatic forces. There are four bases which make up the DNA molecule, thymine (T), adenine (A), cytosine (C), and guanine (G). In two of the bases, thymine and adenine, an oxide ion with a single negative charge (O) from the thymine base is attracted to a hydrogen ion (H*) from the adenine ion. The distance between the two ions is 28.0 nm. Note that the oxide ion has a charge equivalent to a negative elementary charge and the hydrogen ion is equivalent to a positive elementary charge. 1. What is the strength of the electrostatic force between these two ions? 2. What is the direction of the force exerted on the oxide ion by the hydrogen ion? (Assume that the oxide ion is to the right of the hydrogen ion.) 3. How many hydrogen ions would it take to equal the amount of charge contained in a lightning bolt, 25 coulombs