SPH 102
TOPIC TWO
CHARGE AND COULOMB’S LAW
2.1 Electric charge
▪ A plastic rod rubbed in fur or silk and then placed close to small pieces of paper attracts the small pieces. This attraction is due to the electric charge we set up on the rod when it is in contact with the silk or fur. Electric charge is an intrinsic property of the fundamental particles that make up objects such as rods, silk, and fur.
▪ When we rub the glass rod with a silk cloth, some negative charges flow from the rod to the silk, leaving the rod with some excess positive charges. We rub the silk over the rod to increase the number of contact points and, thus, the number of transferred charges. On the other hand, when plastic is rubbed in fur, it gains excess negative charge from the fur.
▪ There are two types of electric charges: positive and negative. The two types of electric charge were named by the American scientist and statesman Benjamin Franklin.
▪ In most everyday objects, there are about equal numbers of negatively charged particles and positively charged particles. So, the net charge is zero, the charge is said to be balanced, and the object is said to be electrically neutral.
▪ If a body acquires excess charges (positive or negative) through, for example, rubbing, the number of positive charges in it will not be the same as the number of negative charges, and the body is then said to be charged.
▪ Like charges repel, while unlike charges attract. This is the law of electrostatic charges, where the term electrostatic emphasizes that, relative to each other, the charges are either stationary or moving only very slowly.
Figure 2.1 shows a demonstration of the electrostatic law of charges.
a b c
Figure 2.1: The law of electrostatic charges. (a) Like charges repel and (b) Unlike charges attract
2.2 Conductors and insulators
▪ Materials can be classified according to the ability of the charge to move through them. Conductors are materials through which charges can move relatively freely. Examples include metals, the human body, and tap water.
▪ Nonconductors/ insulators are materials through which charge cannot move freely. Examples include rubber, plastic, glass, and chemically pure water.
▪ Semiconductors are materials that are intermediate between conductors and insulators. Examples include silicon and germanium in computer chips. Superconductors are materials that are perfect conductors, allowing charge to move through them without any hindrance.
Conduction can eliminate excess charges on an object. If you rub a copper rod with wool, the charge is transferred from the wool to the rod. However, if you are holding the rod while also touching a faucet, you cannot charge the rod despite the transfer. The reason is that you, the rod, and the faucet are all conductors connected to Earth’s surface, which is a considerable conductor. Because the excess charges put on the rod by the wool repel one another, they move away from one another by moving first through the rod, then through you, and then through the faucet to reach Earth’s surface, where they can spread out. The process leaves the rod electrically neutral.
▪ In thus setting up a pathway of conductors between an object and Earth’s surface, we are said to ground the object, and in neutralizing the object (by eliminating an unbalanced positive or negative charge), we are said to discharge the object.
▪ If instead of holding the copper rod in your hand, you hold it by an insulating handle, you eliminate the conducting path to Earth, and the rod can then be charged by rubbing (the charge remains on the rod), as long as you do not touch it directly with your hand.
▪ The properties of conductors and insulators are due to atoms’ structure and electrical nature. Atoms contain positively charged protons, negatively charged electrons, and electrically neutral neutrons. The protons and neutrons are packed tightly together in a central nucleus.
▪ The charge of a single electron and that of a single proton have the same magnitude but are opposite in sign. Hence, an electrically neutral atom contains equal numbers of electrons and protons.
Electrons are held near the nucleus because they have the electrical sign opposite that of the protons in the nucleus and thus are attracted to the nucleus. When atoms of a conductor like copper come together to form the solid, some of their outermost ( and so most loosely held) electrons become free to wander about within the solid, leaving behind positively charged atoms ( positive ions). We call the mobile electrons conduction electrons. There are few (if any) free electrons in a nonconductor.
▪ The experiment in figure 2.1c demonstrates the mobility of charge in a conductor. A negatively charged plastic rod will attract either end of an isolated neutral copper rod. What happens is that many of the conduction electrons in the closer end of the copper rod are repelled by the negative charges on the plastic rod. Some of the conduction electrons move to the far end of the copper rod, leaving the near end depleted in electrons and, thus, with an unbalanced positive charge. This positive charge is attracted to the negative charges in the plastic rod. Although the copper rod is still neutral, it is said to have an induced charge, meaning that some of its positive and negative charges have been separated due to a nearby charge.
▪ Similarly, if a positively charged glass rod is brought near one end of a neutral copper rod, the induced charge is again set up in the neutral copper rod, but now, the near end gains conduction electrons, becomes negatively charged, and is attracted to the glass rod, while the far end is positively charged.
2.3 Coulomb’s law
▪ If two charged particles are brought near each other, they each exert an electrostatic force on each other. The direction of the force vectors depends on the signs of the charges. If the particles have the same charge sign, they repel each other. That means that the force vector on each is directly away from the other particle (figure 2.2 a and b). If we release the particles, they accelerate away from each other.
2.2: Two charged particles repel each other if they have the same charge sign, either (a) both positive or (b) both negative. (c) They attract each other if they have opposite signs of charge (d) the electrostatic force on particle 1 in terms of a unit vector along an axis through the two particles, radially away from particle 2.
▪ If, instead, the particles have opposite signs of charge, they attract each other. That means that the force vector on each is directed toward the other particle (figure 2.2c). If we release the particles, they accelerate toward each other.
▪ The equation for the electrostatic forces acting on the particles is called Coulomb’s law after Charles-Augustin de Coulomb.
The equation applies to particles.
▪ It can be written in vector form in terms of the particles 1 and 2 of charge q1 and q2, respectively (figure 2.2d). (These symbols can represent either a positive or negative charge.)
▪ Let’s focus on particle one and write the force acting on it in terms of a unit vector that points along a radial axis extending through the two particles, radially away from particle 2. The electrostatic force is written as:
…………………….….. (2.1a)
where r is the separation distance between the two particles and k is an electrostatic / Coulomb constant. If q1 and q2 have the same sign, then the product q1q2 gives a positive result. So, equation 2.1a tells us that the force on particle 1 is in the direction of rො. That checks because particle one is being repelled from particle 2. If q1 and q2 have opposite signs, the product q1q2 gives us a negative result.
▪ The form of equation 2.1a is the same as that of Newton’s equation for the gravitational force between two particles with
masses m1 and m2 and separation r:………………….….. (2.1b)
▪ Although the two types of forces are different, both describe inverse square law (the 1/r2 dependences) that involves a product of a property of the interacting particles, the charge in one case and the mass in the other. However, the equations differ in that gravitational forces are always attractive, but electrostatic forces may be either attractive or repulsive, depending on the signs of the charges. This difference arises from the fact that there is only one type of mass but two types of charge.
▪ The SI unit of charge is the Coulomb. The electrostatic constant k in equation 2.1a is often written as: The quantity
