Electric Charge & Electric Field PDF

Electric Charge & Electric Field Lesson 1 Who Discovered Electricity? Electricity's discovery is not attributed to a single individual; it's a story of collective breakthroughs. From Thales of Miletus's ancient observations to Benjamin Franklin's iconic kite experimen...

Electric Charge & Electric Field Lesson 1 Who Discovered Electricity? Electricity's discovery is not attributed to a single individual; it's a story of collective breakthroughs. From Thales of Miletus's ancient observations to Benjamin Franklin's iconic kite experiment, to Michael Faraday's advancements in electromagnetism. The known history of electricity goes back to at least 620-550 BCE, when, in ancient Greece, it was found that rubbing fur on amber caused an attraction between the two. This discovery is credited to the philosopher Thales of Miletus. It was to be many centuries before anyone was able to connect this phenomenon with lightning, and a century more before electrical currents were put to practical use. Benjamin Franklin is perhaps the name most associated with electricity. In 1750, he sought to prove that lightning was caused by electricity by describing an experiment in which an electrical conductor would be used to extract power from a thundercloud. It seems that before he was able to carry this out, a French experimenter named Thomas-Francois Dalibard, who had read Franklin’s writings on the subject, successfully obtained an electrical discharge from a thundercloud using a 40 foot (12.2 meter) metal pole in May 1752. Franklin is credited with carrying out a similar experiment in June of that year, in which he flew a kite with a metal key attached to it into a suitable cloud. The precise historical details are unclear, but he may have then retrieved the key and discharged electricity from it. What is an Electric Charge? Electric charge can be defined as a fundamental property of subatomic particles that gives rise to the phenomenon of experiencing force in the presence of electric and magnetic fields. These fields exert influence on charged particles, resulting in observable effects. TYPES OF ELECTRIC CHARGE Electric charge comes in two main types: positive and negative charges. Positive charges are associated with protons, which are subatomic particles residing in the nucleus of an atom. They are represented by the symbol “+”. On the other hand, negative charges are linked to electrons, which orbit the atomic nucleus and are denoted by the symbol “-“. The distinction between positive and negative charges plays a vital role in comprehending the behaviour of electrically charged objects. Opposite charges, such as positive and negative, attract each other, while like charges, such as positive and positive or negative and negative, repel each other. ELECTRIC ATTRACTION AND REPULSION The attraction and repulsion of two charged objects are sometimes summarized as “Like charges repel, and opposite charges attract.” When an object carries a negative charge, it possesses an excess of electrons compared to protons. Conversely, a positive charge indicates an excess of protons relative to electrons. It’s important to note that when an equal number of positive and negative charges are present, they cancel each other out, resulting in a neutral state for the object. Is Electric Charge a Vector Quantity? it is a scalar quantity. While vectors have both magnitude and direction and obey vector addition laws like the triangle law and parallelogram law, electric charge does not exhibit these properties. When currents meet at a junction, the resulting current is determined by the algebraic sum of the individual currents rather than their vector sum. Thus, electric charge is considered a scalar quantity, despite having magnitude and direction. MEASURING ELECTRIC CHARGE Coulomb is the unit of electric charge, Q. “One coulomb is the quantity of charge transferred in one second.” Mathematically, the definition of a coloumb is represented as: Q = It  Ampere is defined as the unit of electric current that is equal to the flow of one Coulomb per second. Ampere is named after the French Physicist and Mathematician Andre-Marie Ampere. One ampere of current represents one coulomb of electrical charge, i.e. 6.24×1018 charge carriers, moving in one second. The relationship between ampere and coulomb is represented as follows: Ampere = 1 Coulomb / Second At any given point in an area experiencing current, the Ampere value will increase proportionately if the charge on particles moving through it increases. PROPERTIES OF ELECTRIC CHARGE Additivity of Electric Charge Let us consider a system of charges containing three point charges with magnitudes q , q and 1 2, q. In such a system, the total charge of the 3 system can be obtained by algebraically adding the three charges. Q = q 1 + q2 + q 3 For example, if we have a positive charge of +3 units and a negative charge of -2 units, the resulting charge would be +1 unit. Conservation of Electric Charge In an isolated system, electric charge is conserved. This means that the total electric charge within the system remains constant over time. The algebraic sum of all the charges present in the system remains the same. Conservation of Electric Charge According to the principle of conservation of charges, the charges are neither created nor destroyed; they are only transferred from one body to the other. Quantization of Electric Charge According to the principle of quantization of electric charge, all the free charges are integral multiples of a basic predefined unit, which we denote by e. Thus, the charge possessed by a system can be given as, Where n is an integer (zero, a positive or a negative q = ne number) and e is the basic unit of charge, that is, the charge carried by an electron or a proton. The value of e is 1.6 × 10-19C. ELECTRIC CHARGE Thus, 1 coulomb = 6.242 x 𝟏𝟎𝟏𝟖 e Thus, 1 electron = 1.6022 x 10-19 C  COULOMB’S LAW ▪ The force between two charges gets stronger as the charges move closer together. ▪ The force also gets stronger if the amount of charge becomes larger.  q1 q2 F= k 2 r Where; ✓ Fe is the electric force, ✓ q1 and q2 are electric charges, ✓ k is the Coulomb’s constant 8.988×109 N⋅m2/C2 and or 9.0×109 N⋅m2/C2 ✓ r is the distance of separation. Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects. The electrostatic force is a vector quantity and is expressed in units of Newtons (N). The force is understood to be along the line joining the two charges.  ELECTRIC FORCE The force between the charged objects is an electric force. The size of the electric force depends on 2 things: 1. The amount of charge (the greater the charge, the greater the force) 2. The distance between charges (the further the distance, the less the force) Derivation of Coulomb’s Law Formula  Coulomb’s Law 𝟐 Charge 2 , 𝒒𝟐 Electric Force , F Distance , 𝒓 Charge 1 , 𝒒𝟏 𝒌|𝒒𝟏 𝒒𝟐 | 𝒌|𝒒𝟏 𝒒𝟐 | 𝟐 𝒓 = 𝑭𝒓𝟐 𝑭𝒓𝟐 𝑭= 𝑭 𝒒𝟏 = 𝒒𝟐 = 𝒓𝟐 Note: 𝒌𝒒𝟐 𝒌𝒒𝟏 Final answer MUST NOT be squared. 𝒌|𝒒𝟏 𝒒𝟐 | 𝒓= 𝑭  Quantization of Charge Charge , q No. of electrons , n Electrons , e 𝒒 𝒒 𝒒 = 𝒏𝒆 𝒏= 𝒆= 𝒆 𝒏 SAMPLE PROBLEM. 1) A negative charge of 4.0 C and a positive charge of 6.0 C are separated by 75 m. What is the force between the two charges? SAMPLE PROBLEM. 2) A negative charge of 0.0005 C exerts an attractive force of 9.0 N on a second charge that is 10 m away. What is the magnitude of the second charge? SAMPLE PROBLEM. 3) By how much does the electric force between a pair of charged bodies diminish when their separation is doubled? tripled? How Can You Charge Objects? Methods of Charging The process of supplying electric charge to an object or causing it to lose electric charge is referred to as charging. There are three distinct methods by which an initially uncharged object can acquire charge: 1) Charging by friction 2) Charging by conduction 3) Charging by induction **In each of these, only the electrons move. The protons stay in the nucleus** Charging by Friction When two objects are rubbed against each other, a transfer of charge occurs. In this process, one of the objects loses electrons while the other gains electrons. The object losing electrons becomes positively charged, while the object gaining electrons becomes negatively charged. This phenomenon, where both objects become charged due to friction, is commonly known as electrification by friction. For example, when a plastic rod is rubbed with a piece of cloth, electrons are transferred from the rod to the cloth. As a result, the rod becomes positively charged and the cloth becomes negatively charged. Charging by Conduction Charging by conduction involves bringing an uncharged object in close proximity to a charged object. If the charged object has an unequal number of protons and electrons, the uncharged object will discharge electrons to achieve stability. This transfer of charge through contact is known as charging by conduction. Charging by conduction Charging by conduction refers to the technique of charging an uncharged material by bringing it into touch with some other charged material. A negatively as well as positively charged item seems to have an uneven amount of charges. Charging by conduction As a consequence, whenever a charged item comes into interaction with an uncharged conductor, electrons are transferred from the charged object toward the conductor. Charging by conduction Whenever a negative object is being utilized just to charge a neutral object, both things become negatively charged, as well as vice versa. Some substances, such as metals and salty water, allow charges to move through them with relative ease. Some of the electrons in metals and similar conductors are not bound to individual atoms or sites in the material. These free electrons can move through the material much as air moves through loose sand. Any substance that has free electrons and allows charge to move relatively freely through it is called a conductor. The moving electrons may collide with fixed atoms and molecules, losing some energy, but they can move in a conductor. Superconductors allow the movement of charge without any loss of energy. Salty water and other similar conducting materials contain free ions that can move through them. An ion is an atom or molecule having a positive or negative (nonzero) total charge. In other words, the total number of electrons is not equal to the total number of protons. Therefore, charging through conduction involves direct interaction with charged as well as uncharged bodies, and related items accumulate a very similar type of charge. Charging by Induction Charging by induction refers to the process of charging an uncharged object by merely bringing it close to a charged object, without any direct physical contact. Through induction, the charged object induces a redistribution of charges in the uncharged object, resulting in the acquisition of charge. Charging by induction method is used in real life in charging microphones, smartphones etc. In smartphones, both the phone and the charging dock contain induction coils of iron wrapped with copper wire. When we place the phone on the charging dock an electromagnetic field is produced between the induction coils. Once the electromagnetic field is produced, electricity is able to pass between the two induction coils, charging the phone wirelessly. Q1 What is electric charge? Electric charge is a fundamental property of matter. It refers to the intrinsic property of particles that gives rise to electric forces and interactions. Q2 How are electric charges distributed within the atom? Within an atom, electric charges are distributed among subatomic particles. Protons, found in the nucleus, carry positive charges, while electrons, which orbit the nucleus, carry negative charges. Neutrons, also present in the nucleus, have no electric charge. Q3 What are the positively charged subatomic particles called? The positively charged subatomic particles are called protons. They have a positive electric charge. When the matter has more protons than electrons, then it is said to have a positive charge. Q4 When will an electric charge be negative? An electric charge will be negative when an object has an excess of electrons. Q5 Why is an electric charge a scalar quantity? When two currents meet at a junction, the resultant current of these will be an algebraic sum and not the vector sum. Therefore, an electric current is a scalar quantity. Q6 What is the unit for measuring electric charge? The unit for measuring electric charge is the coulomb (C). It is named after the French physicist Charles-Augustin de Coulomb. Q7 Define one coulomb. One coulomb is the quantity of charge transferred in one second. Q8 What are the types of electric charges? The two types of electric charges are positive and negative charges. Positive charges are associated with protons, while negative charges are associated with electrons. Q9 How is an uncharged object charged? An uncharged object can be charged through various methods, such as charging by friction (rubbing two objects together), charging by conduction (contact with a charged object), or charging by induction (bringing an uncharged object close to a charged object without direct contact). Q10 What are the other units of electric charge? Faraday and Ampere-Hour are the other units of electric charge. Apart from the coulomb, smaller units of electric charge include the microcoulomb (μC), nanocoulomb (nC), and picocoulomb (pC). These units are used to measure smaller quantities of electric charge. Electric Field Lesson 2 An Electric field can be considered an electric property associated with each point in the space where a charge is present in any form. An electric field is also described as the electric force per unit charge. Electric fields are usually caused by varying magnetic fields or electric charges. ELECTRIC FIELD INTENSITY → → F Electricforce in Newton acting on Where, E is E= the charge placed electric field q0 at the point. intensity Magnitude of the charge in coulomb ELECTRIC FIELD INTENSITY → → F E= q0 We can define the electric field as the force per unit charge placed within that field.  Situation Value Inside a copper wire of household circuits 10-2 N/C Near a charged comb 103 N/C Inside a TV picture tube 105 N/C Near the charged drum of a photocopier 105 N/C Electric breakdown across an air gap 3×106 N/C At the electron’s orbit in a hydrogen atom 5×1011 N/C On the suface of a Uranium nucleus 3×1021 N/C September 18, 2007 ELECTRIC FIELD INTENSITY → → F E= q0 Thus, the unit for electric field intensity is Newton per Coulomb, N/C ELECTRIC FIELD INTENSITY Therefore, the magnitude of the electric field is given by the equation: 𝑬=𝒌 𝑸 𝒓𝟐 𝑵.𝒎𝟐 𝑪 = 𝑪𝟐 𝒎𝟐 𝑵 = 𝑪 ELECTRIC FIELD INTENSITY It is the same with electric fields and forces. The magnitude of the electrostatic force 𝑭𝒆 is proportional to the magnitude of the electric field E.  FOUR IMPORTANT PROPERTIES OF ELECTRIC FIELD LINES. 1) The field lines must be tangent to the direction of the field at any point. 2) The greater the line density, the greater the magnitude of the field. 3) The lines always start from the positively charged objects and end on negatively charged objects. 4) The line must never cross. Derivation of Electric Field Intensity Formula  Electric Field Intensity Electric Field Intensity, E Force, F Charge , q 𝑭 𝑭 𝑬= 𝑭 = 𝑬𝒒 𝒒= 𝒒 𝑬  Electric Field Intensity Electric Field Intensity, E Charge , q Distance , 𝒓𝟐 𝒌𝑸 𝑬𝒓 𝟐 𝟐 𝒌𝑸 𝑬= 𝟐 𝒒= 𝒓 = 𝒓 𝒌 𝑬 SAMPLE PROBLEM. 1) What is the magnitude of a point charge whose E-field at a distance of 15 cm is 2.3 N/C? SAMPLE PROBLEM. 2) A small charge, 6.0 x 10^-3 C is found in a uniform e-field of 1.8 N/C. Determine the force on the charge. SAMPLE PROBLEM. 3) An electron and a proton are each placed at rest in an electric field of 1040 N/C. How much is the magnitude of the force?