Physics II Lecture Notes (PHYS233) Chapter 21 Electric Charge and Electric Field PowerPoint® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and PowerPoint® Lectures for Roger A. Freedman Lectures by University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Wayne Anderson Copyright © 2012 Pearson Education Inc. Lectures by Wayne Anderson Copyright © 2012 Pearson Education Inc. Electric Charge and Electric Field Edited By: Dr. Dastan Khalid Dr. Rebar T. Abdulwahid rebar.abdulwahid@auis.edu.krd Goals for Chapter 21 • To study electric charge and charge conservation. • To see how objects become charged. • To calculate the electric force between objects using Coulomb’s law. • To learn the distinction between electric force and electric field. • To calculate the electric field due to many charges. • To visualize and interpret electric fields. • To learn the properties of electric dipoles. Copyright © 2012 Pearson Education Inc. Introduction • Water makes life possible as a solvent for biological molecules. What electrical properties allow it to do this? • We now begin our study of electromagnetism, one of the four fundamental forces. • We start with electric charge and look at electric fields. Copyright © 2012 Pearson Education Inc. Electric charge • Two positive or two negative charges repel each other. A positive charge and a negative charge attract each other. • Figure 21.1 below shows some experiments in electrostatics. Copyright © 2012 Pearson Education Inc. Laser printer • A laser printer makes use of forces between charged bodies. Copyright © 2012 Pearson Education Inc. Electric charge and the structure of matter • The particles of the atom are the negative electron, the positive proton, and the uncharged neutron. • Protons and neutrons make up the tiny dense nucleus which is surrounded by electrons (see Figure 21.3 at the right). • The electric attraction between protons and electrons holds the atom together. Copyright © 2012 Pearson Education Inc. Atoms and ions • A neutral atom has the same number of protons as electrons. • A positive ion is an atom with one or more electrons removed. A negative ion has gained one or more electrons. Copyright © 2012 Pearson Education Inc. Conservation and quantization of charge • The proton and electron have the same magnitude charge. • The magnitude of charge of the electron or proton is a natural unit of charge. All observable charge is quantized in this unit. • That is, electric charge exists as discrete “packets” and we can write q = Ne Where N is some integer ; e = 1.602 × 10-19 C • The universal principle of charge conservation states that the algebraic sum of all the electric charges in any closed system is constant. Copyright © 2012 Pearson Education Inc. Conductors and insulators • A conductor permits the easy movement of charge through it. An insulator does not. • Most metals are good conductors, while most nonmetals are insulators. (See Figure 21.6 at the right.) • Semiconductors are intermediate in their properties between good conductors and good insulators. Copyright © 2012 Pearson Education Inc. Charging by induction • In Figure 21.7 below, the negative rod is able to charge the metal ball without losing any of its own charge. This process is called charging by induction. Copyright © 2012 Pearson Education Inc. Electric forces on uncharged objects • The charge within an insulator can shift slightly. As a result, two neutral objects can exert electric forces on each other, as shown in Figure 21.8 below. Copyright © 2012 Pearson Education Inc. Electrostatic painting • Induced positive charge on the metal object attracts the negatively charged paint droplets. Copyright © 2012 Pearson Education Inc. Coulomb’s law • Coulomb’s Law: The magnitude of the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. (See the figure at the right.) • Mathematically: q1 and q2 are point particles carrying charges. ๐๐ ๐๐ ๐ ๐๐ ๐๐ r is the separation between q1 and q2. ๐ญ = ๐ ๐๐ = ๐๐ ๐ ๐๐ k is the Coulomb constant ๐ × ๐๐๐ ๐ต. ๐ ๐ /๐ช๐ . ๐ Copyright © 2012 Pearson Education Inc. ๐๐ is permittivity of free space. Measuring the electric force between point charges • The figure at the right illustrates how Coulomb used a torsion balance to measure the electric force between point charges. Copyright © 2012 Pearson Education Inc. Example 21.1 Coulomb’s Force vs Newton’s Gravitation Force ๐ญ๐ = ๐ ๐ญ๐ = ๐ฎ ๐๐ ๐๐ ๐๐ ๐๐ ๐๐ ๐๐ Coulomb’s force Gravitational force k = ๐ × ๐๐๐ ๐ต. ๐ ๐ /๐ช๐ G =๐. ๐๐ × ๐๐−๐๐ ๐ต. ๐ ๐ /๐๐๐ Copyright © 2012 Pearson Education Inc. Example 21.2 Copyright © 2012 Pearson Education Inc. Example 21.3 Copyright © 2012 Pearson Education Inc. Vector addition of electric forces in a plane • Example 21.4: Two equal positive charges q1 = q2 = 2µC are located at (x,y) plane (0,3)m and (0,-3) m respectively. What are the magnitude and direction of the total electric forces exerted by q1 and q2 on Q = 4µC at (4,0). Copyright © 2012 Pearson Education Inc. Electric field • A charged body produces an electric field in the space around it. • We use a small test charge q0 to find out if an electric field is present Copyright © 2012 Pearson Education Inc. Definition of the electric field • The electric field ๐ฌ at a point in space is defined as the electric force ๐ญ๐ acting on a positive test charge qo placed at that point divided by the magnitude of the test charge: ๐ญ๐ ๐ฌ= ๐๐ Unit of ๐ฌ is (N/C) Copyright © 2012 Pearson Education Inc. Electric field of a point charge • By definition, the electric field of a point charge always points away from a positive charge but towards a negative charge. • To find the electric field due to a point charge q (or charged particle) at any point a distance r from the point charge from Coulomb's law, the electrostatic force acting on qo is: ๐ญ = ๐ ๐ ๐๐ ๐๐ ๐บ๐ ๐๐ ๐เท • The direction of F is directly away from the point charge if q is positive, and directly toward the point charge if q is negative. The electric field vector is: ๐ฌ= ๐ญ ๐๐ = ๐ ๐ ๐๐ ๐เท Copyright © 2012 Pearson Education Inc. = ๐ ๐ ๐๐ ๐๐ ๐๐ ๐เท ( point charge) Electric-field magnitude for a point charge Copyright © 2012 Pearson Education Inc. Electric-field vector of a point charge Copyright © 2012 Pearson Education Inc. Example: Electron in a uniform field The strength of the electric field in the region between two parallel deflecting plates (one positive and the other negative) of a cathode-ray oscilloscope is 25 kN/C. (a) Determine the force exerted on an electron passing between these plates. (b) What acceleration will the electron experience in this region? d + a A - + - + + + Copyright © 2012 Pearson Education Inc. - - b Superposition of electric fields • The total electric field at a point is the vector sum of the fields due to all the charges present. • Therefore, the net electric field at the position of the test charge is Copyright © 2012 Pearson Education Inc. Superposition of electric fields • Homework : (b) and (c) Copyright © 2012 Pearson Education Inc. Electric Field due to continuous charge distribution : In many cases the distances between charges in a group of charges are much smaller than the distance from a point where the electric field is to be calculated. In such situations, the system of charges can be modeled as continuous. That is, the system of closely spaced charges is equivalent to a total charge that is continuously distributed along some line, over some surface, or throughout some volume. The electric field at P due to a continuous charge distribution is the vector sum of the fields โ๐ธ due to all the elements โ๐ of the charge distribution. Copyright © 2012 Pearson Education Inc. Electric Field due to continuous charge distribution : The electric field at P due to one charge element carrying charge Δq is The total electric field at P due to all elements in the charge distribution is approximately where the index i refers to the ith element in the distribution. Because the charge distribution is modeled as continuous, the total field at P in the limit Δq → 0 is Copyright © 2012 Pearson Education Inc. Electric Field due to continuous charge distribution: • If a charge Q is uniformly distributed along a line of length โ, the linear charge density λ is defined by ๐ ๐ธ โ = where λ has units of coulombs per meter (C/m). • If a charge Q is uniformly distributed on a surface of area A, the surface charge density σ is defined by ๐ = ๐ธ ๐จ where σ has units of coulombs per square meter (C/m2). • If a charge Q is uniformly distributed throughout a volume V, the volume charge density ρ is defined by ๐ = ๐ธ ๐ฝ where ρ has units of coulombs per cubic meter (C/m3). Copyright © 2012 Pearson Education Inc. Electric Field due to continuous charge distribution: The Electric Field Due to a Charged Rod (1) Let us consider a positively charged rod is placed along x-axis, extended from 0 to L as shown in the figure. Suppose the charge is distributed uniformly, and we want to find the electric field E at point p which a apart from the rod. y a dx 0 Copyright © 2012 Pearson Education Inc. x x+d x L x P Electric Field due to continuous charge distribution: The Electric Field Due to a Charged Rod (2) Let us divide the rod into many small pieces of infinitesimal size and take one of them. The length of the pieces is dx and it has a charge of dq and linear charge density λ. The charge dq on the small segment is dq = λ dx So the electric field due to this small segment is given by ๐ ๐ฌ = ๐ ๐ ๐ ๐ (๐ณ+๐ −๐)๐ ๐ฦธ (๐ฦธ is unit vector along x-axis) Because every other element also produces a field in the positive xdirection, the problem of summing their contributions is particularly simple in this case. The total field at P due to all segments of the rod, which are at different distances from P, is given by ๐ณ ๐ณ ๐ ๐ ๐ ๐ ๐ ๐ฌ=๐ เถฑ ๐ฦธ = ๐๐๐ฦธ เถฑ ๐ ๐ (๐ณ + ๐ − ๐) ๐ ๐ (๐ณ + ๐ − ๐) Copyright © 2012 Pearson Education Inc. Electric Field due to continuous charge distribution: The Electric Field Due to a Charged Rod (3) Where the limits on the integral extend from one end of the rod (x= 0) to the other (x =L). Carrying out the integral we get ฦธ ๐๐ณ ๐๐๐ธ ฦธ ๐ฌ = ๐๐ = ๐(๐ณ + ๐) ๐(๐ณ + ๐) Where we have used the fact that the total charge ๐ธ = ๐๐ณ *Suppose we move to a point P very far away from the rod. What is the nature of the electric field at such a point? Copyright © 2012 Pearson Education Inc. Field of a ring of charge: Example 21.9 Positive charge Q is uniformly distributed around a conducting ring of radius a. Calculate the electric field at a point P along the axis of the ring at a distance x from its center. In terms of the linear charge density ๐ = Q/2π๐ and ๐๐ = ๐๐๐ Net field ๐ ๐ฌ, are directed along the x-axis (y-axis component cancel each other) Copyright © 2012 Pearson Education Inc. Field of a charged line segment Homework: Consider a positively charged rod is placed along x-axis, extended from -L to L as shown in the figure. Suppose the charge is distributed uniformly, find the electric field E at point p which a apart from the rod. Copyright © 2012 Pearson Education Inc. Electric field lines • An electric field line is an imaginary line or curve whose tangent at any point is the direction of the electric field vector at that point. (See Figure 21.27 below.) Copyright © 2012 Pearson Education Inc. Electric field lines of point charges • Figure 21.28 below shows the electric field lines of a single point charge and for two charges of opposite sign and of equal sign. Copyright © 2012 Pearson Education Inc. The properties of electric field lines may be summarized as follows 1) Electrostatic field lines always start on positive charges and end on negative charges. 2) The number of lines originating from, or terminating on, a charge is proportional to the magnitude of the charge. 3) The direction of the field at a point is given by the tangent to the field line at that point. 4) The field strength is equal to the density of lines, that is the number of lines per unit area (where the area is on a surface normal to the field). 5) No two field lines can cross each other; otherwise the field would be pointing in two different directions at the same point. Copyright © 2012 Pearson Education Inc. Electric Dipole moment A pair of equal and opposite charges separated by some distance is known as an electric dipole. The product of the charge q and the separation d is the magnitude of a quantity called the electric dipole moment (p), ๐ = ๐๐ ๐ = ๐ × ๐ฌ ; ๐ = ๐๐ฌ ๐๐๐ ๐ Copyright © 2012 Pearson Education Inc.
