Introduction. Strand G Unit 1: Electrostatics. Learning Objectives. Introduction.

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1 Learning Objectives At the end of this unit you should be able to Define charge and state the charge on an electron and proton Categorise materials into groups depending on their ability to convey charge Explain how insulators may be charged by rubbing Use Coulomb s Law to calculate the force between charges and determine whether the force is attractive or repulsive Explain the concept of an electric field Calculate the electric field strength at a point from the force experienced from a charge Construct field diagrams of single point charges and systems containing two point charges. Since classical times, it has been known that some materials when rubbed, will attract tiny dust particles. Amber is a good example of such a material, and it is no coincidence that the Greek word for amber is electron. The attraction or repulsion of particles that a material exhibits after rubbing is an example of the electrostatic force between charged objects or particles. This force can be negative or positive, and is much stronger than gravity (for example, if you rub a balloon on your jumper you can then defy gravity by sticking the balloon to a wall). Charles Augustin de Coulomb ( ) studied the interaction forces of charged particles in detail in In fact, the unit of charge was named after him in recognition of his work. Coulomb found that for point charges (charges that are very small in comparison to the distances between them), the force between them was attractive or repulsive depending on the sign of the charge. In addition, he found that the magnitude of the force between charges reduced as the distance between the charges increased. Specifically, he found that the magnitude of the force reduced by a factor of four whenever he doubled the distance between the charges, and increased by a factor of 4 whenever he halved the distance between the charges. This relationship is now known as Coulomb s Law.

2 Key Facts and Principles. Electrical charge is as fundamental quantity. Objects with electrical charge are accelerated by electric force. Charge is measured in Coulombs (C), and the charge of the particles that constitute an atom is as follows, listed together with their respective mass; Particle Charge (C) Mass (Kg) Proton (p) Neutron (n) Electron (e) Any charged system has a total charge that is a multiple of C. Relative charge is often assigned such that the charge of a proton is +1, a neutron 0, and an electron -1. In this way a relative charge of +2 is equal to C = C. Single charges are usually denoted by either the symbol q which can be either negative or positive, or by the particle symbol (p for proton and e for electron). Overall charge (which tends to be a large number of individual charges) is denoted by the symbol Q. The atoms in a conductor have electrons that are loosely bound to the nucleus. These spare loosely bound charges are free to move through the material, conveying charge (conduct electricity). The electrons of a semi-conductor are more tightly bound. However, when heated the electrons have enough energy to break free from the atoms and move through the material, and the semi-conductor becomes conducting. Insulators, such as plastics, have electrons that are very tightly bound to atoms. Insulators do not conduct electricity since they have no free charges to do so. The interaction between charges that are at rest (or nearly at rest) is known as electrostatics. Insulators can be charged with a static (stationary) charge. Rubbing a polythene rod with a dry cloth: Electrons transferred to the surface atoms of the rod. Polythene rod now has more electrons, and is negatively charged. The dry cloth has given up electrons. It is therefore positively charged relative to the rod. Note that being positively charged can mean an absence of negative charge.

3 Rubbing a Perspex rod with a dry cloth: Electrons transferred from the rod to the surface atoms of the dry cloth. The Perspex rod gives up electrons and is therefore positively charged The cloth gains electrons becoming negatively charged. Some insulators become negatively charged and some positively charged when rubbed, depending on how much the atoms of the material want to gain or lose electrons. Two positive charges or two negative charges repel each other A positive charge and negative charge attract each other Like sign charges repel and opposite sign charges attract. Hence there is a force between the charges. If the charges q1 and q2 are either both positive or both negative, the force is repulsive. If either one of the charges is positive whilst the other is negative, the force is attractive. The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, FF = qq 1qq 2 4ππεε 0 rr 2 where F = electrostatic force q = point charge (in coulombs) r = distance between charges (in metres) ε0 = constant = C 2 /Nm 2 The force between charges always acts along a line joining the two charges. The sign of the force signifies if the force experienced is repulsive ( + ive), or attractive ( - ive). For two charges that exert a force on a third charge, the resultant force acting on the third charge is the vector sum of the forces from the other two charges. The super position of forces applies to any number of charges. To solve a multiple charge problem;

4 Draw a free body diagram of the charge in question and draw the direction of each force, being careful to evaluate if each individual force is repulsive or attractive Calculate the magnitude of the force on the charge in question that is exerted from each of the other charges. Sum the forces acting vectorially just as you would for vector mechanics, either by splitting the individual vectors into components (the easiest method), or by using the head to tail method. The Coulomb repulsion between charges gives rise to a certain static distribution of charge over a surface. For a solid metal volume that is either negatively or positively charged Each charge exerts a repulsive force on all other charges on the volume. The closer the charges are the greater the force of repulsion. To minimize energy, the charges distribute themselves due to this force, such that the maximum distance between nearest neighbours is achieved. The electrons therefore arrange themselves evenly over the surface, not throughout the volume. The electric field E is a concept that describes the region of space around a charge, specifically it describes how much force another charge would experience at that position in space. The electric force experienced by a charge is exerted on it by the electric field created by other charges. The electric field that a point charge creates is radial, since it emanates from a single point in space. The electric field is a vector and has size and direction, with the direction signified by arrows. Electric fields always start on a positive charge and end on a negative charge. The electric field strength E at a point in the field is defined as the force F per unit charge Q on a positive test charge placed at that point or in symbols EE = FF QQ The unit of E is the Newton per Coulomb (NC -1 ).

5 Glossary Algebraic denoting a mathematical expression or equation in which a finite number of symbols are combined using only the operations of addition, subtraction, multiplication, division, and exponentiation Coulomb - the SI unit of electric charge, equal to the quantity of electricity conveyed in one second by a current of one ampere. Coulombic (attraction or repulsion) - The force of attraction or repulsion between positive and negative charges (obeying Coulomb s Law). Electric Field a region of space around a charged particle or object within which a force would be exerted on other charged particles or objects. Electrostatic - relating to stationary electric charges or fields as opposed to electric currents (moving charge). Insulator Any material or device that insulates, where insulates in this context means the absence of electrical conduction. Point Charge A charge with physical dimensions much smaller than the distance between such charges, such that the charge may be approximated to a single point in space without volume. Radial Radiating from or converging to a common centre. Resultant A resultant force is a single or overall force obtained by combining a system of forces that act. Semi-conductor A solid with the electrical property between a conductor and insulator. Usually temperature dependent, providing conduction at high temperatures and electrical insulation at low temperatures.