Federal University Dutsin-Ma PHY102 Physics Lecture Notes PDF

DEPARTMENT OF PHYSICS FACULTY OF PHYSICAL SCIENCE FEDERAL UNIVERSITY DUTSIN-MA SECOND SEMESTER, 2023/2024 ACADEMIC SESSION COURSE CODE: PHY102 COURSE TITLE: GENERAL PHYSICS II (Electricity & Magnetism)...

DEPARTMENT OF PHYSICS FACULTY OF PHYSICAL SCIENCE FEDERAL UNIVERSITY DUTSIN-MA SECOND SEMESTER, 2023/2024 ACADEMIC SESSION COURSE CODE: PHY102 COURSE TITLE: GENERAL PHYSICS II (Electricity & Magnetism) LECTURE NOTE: UNIT I (FUNDAMENTAL FORCES IN NATURE) Different kinds of force exist at macroscopic level such as gravitational force, frictional force, contact force, spring force, buoyant force, viscous force, pressure force, force due to surface tension, electrostatic force, magnetic force, etc. whereas at microscopic level of study we come across nuclear forces, interatomic forces, intermolecular forces, weak forces, etc. All these forces can be classified into four categories, which are known as fundamental forces in nature. They are: (i) Gravitational force (ii) Electromagnetic force (iii) Weak nuclear force (iv) Strong nuclear force That means, any force other than the above four forces can be derived from these four basic forces. (i) Gravitational Force: Newton discovered that any two bodies in universe attract each other. This force of attraction exists by virtue of their masses, and is known as gravitational force of attraction. He found that the gravitational force,F between two particle mass, 𝑚1 and 𝑚2 is directly proportional to their masses and is inversely proportional to the square of the distance between them. That is; 𝑚1 𝑚2 𝐹=𝐺 𝑑2 1 where ‘G’ is a Universal Gravitational Constant. Though this is the weakest force in nature when compared to other types of fundamental forces, it plays vital role in governing the motion of planets around sun, natural satellites (like moon around earth), artificial satellites, etc. (ii) Electromagnetic Force: The force of attraction or repulsion between any two charged particles is known as electrostatic force. If charges 𝒒𝟏 and 𝒒𝟐 are separated by a distance d, in air then the force of attraction or repulsion between them is given by: 1 𝑞1 𝑞2 𝐹= 4𝜋𝜀0 𝑑 2 This is called Coulomb’s law of electric forces. Charges in motion produce magnetic effects and a magnetic field gives rise to a force on a moving charge. In general electric and magnetic effects are inseparable and hence the name – electromagnetic force. In atoms, electromagnetic force between electrons and protons is responsible for several molecular and atomic phenomena. Apart from this, it also plays vital role in the dynamics of chemical reactions, mechanical and thermal properties of materials, tension in ropes, friction, normal force, spring force, Vander Waals force. Example: Consider a block which is placed on a horizontal surface of a table as shown in figure 1.1. The table balances the weight (Mg) and exerts a force which comes from electromagnetic force between charged constituents of atoms or molecules of surface of block and that of the table. Thus a force called normal force acts on block. Figure 1.1 This electromagnetic force is a strong force when compared to the gravitational force. The electromagnetic force between two protons is 1036 times the gravitational force between them for any fixed distance. (iii) Strong Nuclear Force: In general, the nucleus of every atom consists of two elementary particles called protons and neutrons. As neutrons are uncharged and protons are charged, the electric force of repulsion between protons will cause nucleus to break into fragments. But this is not happening, and also we know that nucleus of a non−radioactive element is a stable one. That means there must be some other attractive force which is dominating coulombic force of repulsion between protons and keeping all the particles in nucleus together in stable condition as gravitational force can’t dominate electric force. That new force existing between any two 2 nucleons and which keeps all the particles in nucleus bound together is known as nuclear force. This force is stronger than electromagnetic force and is a charge independent force. Range of these forces is very small and will be of the order of nuclear size (10−21 th portion of size of an atom). (iv) Weak Nuclear Force: This force appears only in certain nuclear processes. A neutron can change itself into a proton by emitting an electron and another elementary particle called antineutrino simultaneously. This process is called 𝛽 − decay. Similarly a proton can also change into neutron by emitting positron and a neutrino. This process is called 𝛽 + decay. The forces which are responsible for these changes are known as weak forces. These forces are weak in nature when compared to nuclear and electromagnetic forces but stronger than gravitational forces. The range of these weak nuclear forces is exceedingly small, of the order of 10−15m. The following table gives us an overall idea about relative strengths and ranges of four fundamental forces. Relative Name Range Operates among strength All objects in the Gravitational force 10−38 Infinite universe Very short, within nuclear size Weak nuclear force 10−13 Elementary particles (~10−15 metre) Electromagnetic 10−2 Infinite Charged particles force Strong nuclear Very short, within nuclear size 1 Nucleons force (~10−15 metre) ELECTROSTATICS In the past, people could only observe a few electrostatic phenomena such as sparks. That was the beginning of the investigation of electricity. Observations show that objects can be “charged“ by rubbing and by contact between charged and uncharged objects. Objects charged in the same way (such as two light balls in the Figure 1.2 that have been charged by a contact with a stab that was previously charged by rubbing with fur or silk) repel from each other. 3  \ Figure 1.2 Objects charged in different ways (such as stabs of different materials rubbed with different materials: Plastic rubbed with fur or glass rubbed with silk) may also attract each other. Thus one can speak of two kinds of electric charges that can be arbitrarily called “positive charge“ and “negative charge“. There are two kinds of charges; positive and negative charges. Like charges repel, unlike ones attract. A charged body is one that has an excess of either positive or negative charges. Electrons carry negative charges. Metals conduct electricity because they contain free electrons. Insulators such as plastics, wood, rubber etc does not conduct electricity because they do not contain free electrons. Normally atoms are not charged, as the charge of their electrons balances the charge of their core (It consists of protons and neutrons). Removing electrons creates a positively charged ion, and placing additional electrons on the atom creates a negatively charged ion as shown in Figure 1.3. Jumping of electrons from one body to the other can cause sparks. Figure 1.3 The force exerted by a charged particle on another charged particle depends on their separation distance, on their velocities and on their accelerations. Consider the special case in which the source charges are stationary. The electric field produced by the stationary source charges is called electrostatic field 4 Electric Charge Electric charge is a fundamental property of matter that gives rise to electric forces and electric fields. It can be positive or negative. Types of Charges: 1. Positive Charge (+): Protons carry a positive charge. They are fundamental particles found in the nucleus of atoms. 2. Negative Charge (-): Electrons carry a negative charge. They orbit the nucleus of atoms. Conservation of Charge: The total electric charge in an isolated system remains constant. Charge is neither created nor destroyed, only transferred from one object to another. Quantization of Charge: Charge comes in discrete units, with the smallest unit being the charge of an electron (approximately \(1.6 \times 10^{-19}\) coulombs). Substances can be classified in terms of the ease with which charge can move about on their surfaces. Conductors are materials in which charges can move about freely; insulators are materials in which electric charge is not easily transported. Electric charge can be measured using the law for the forces between charges (Coulomb’s Law). Charge is a scalar and is measured in coulombs. The coulomb is actually defined in terms of electric current (the flow of electrons), which is measured in amperes; when the current in a wire is 1 ampere, the amount of charge that flows past a given point in the wire in 1 second is 1 coulomb. That is, q = It where, q is in coulombs, if I is in ampere and t is in seconds. When charges are transferred by simple interactions (i.e. rubbing), it is a negative charge which is transferred, and this charge is in the form of the fundamental particles called electrons. The charge of an electron is 1.6022 × 10-19 C. The electron’s charge is -e. The proton has charge +e. The particles found in nature all have charges which are integral multiples of the elementary charge, e: q = ne where n = 0, ±1, ±2. Because of this, we say that charge is quantized. The mass of the electron is me = 9.1094 × 10-31 kg Properties of Charges 1. Like charges repel and unlike charges attract. 2. A charged body attracts to uncharged (neutral) bodies due to electrostatic induction. 5  3. Charge on a body remains unaffected by motion i.e. the charge on a body or particle remains the same whether it is at rest or moving with any velocity. 4. The electric charge is additive. It means that the total charge on an extended body is the algebraic sum of all the charges located at different points in the body. A neutral body has equal amount of positive and negative charges so that the charge on a neutral body is always zero. 5. Charge is conservative i.e. it can neither be created nor destroyed but it can be transferred from one body to another body. This is known as principle of conservation of charge. 6. Charge is quantized i.e. any physically existing charge is an integral multiple of the of the amount of charge on electron. This smallest amount of charge is 1.6 x 10−19 coulomb and is denoted by ‘e’. Thus 𝑞 = 𝑛𝑒 𝑞 or = 𝑛 (an integer) 𝑒 Applications of Electric Charges: - Electronics: Charges are used to carry signals and power in electronic circuits. - Medicine: Techniques like electrocardiography (ECG) and electroencephalography (EEG) utilize electric charges to measure heart and brain activity, respectively. - Industry: Electric charges are used in processes like electroplating and painting. Example A plastic piece rubbed with wool is found to have a negative charge of 5 x10−7 coulomb. Calculate the number of electrons transferred. Solution Given q = 5 x10−7 coulomb 𝑞 5 x10−7 𝑛= = = 3.125 x 1012 𝑒 1.6 x 10−19 Questions 1. What is the total charge of 75.0 kg of electrons? Solution The mass of one electron is 9.11 × 10-31 kg, so that a mass M = 75.0 kg contains 𝑀 75.0 kg 𝑁= = = 8.23 x 1031 electrons 𝑚𝑒 9.11 x 10−31 kg 6 The charge of one electron is -e = -1.60 × 10-19 C, so that the total charge of N electrons is: Q = N(-e) = (8.23 × 1031)(-1.60 × 10-19 C) = -1.32 × 1013 C 2. A point charge of +3.00 × 10-6 C is 12.0 cm distant from a second point charge of -1.50 × 10-6 C. Calculate the magnitude of the force on each charge. Solution Being of opposite signs, the two charges attract one another, and the magnitude of this force is given by Coulomb’s law. |𝑞1 ||𝑞2 | 𝐹=𝐾 𝑟2 𝑁. 𝑚2 (3.00 x 10−6 𝐶)(1.50 x 10−6 𝐶) 𝟗 𝑭 = (𝟖. 𝟗𝟖 𝐱 𝟏𝟎 ) = 2.81 𝑁 𝐶2 (12.0 x 10−2 m)2 Each charge experiences a force of attraction of magnitude 2.81 N. 7