Lesson 3. Electric Potential. Capacitors Current Electricity

Size: px

Start display at page:

Download "Lesson 3. Electric Potential. Capacitors Current Electricity"

Carol Hawkins
5 years ago
Views:

1 Electric Potential Lesson 3 Potential Differences in a Uniform Electric Field Electric Potential and Potential Energy The Millikan Oil-Drop Experiment Capacitors Current Electricity Ohm s Laws Resistance

2 Potential Difference and Electric Potential When analyzing electric and magnetic fields, it is common practice to use the notation ds to represent an infinitesimal displacement vector that is oriented tangent to a path through space. This path may be straight or curved, and an integral performed along this path is called either a path integral or a line integral (the two terms are synonymous). For an infinitesimal displacement ds of a charge, the work done by the electric field on the charge is F. ds = q 0 E. ds. As this amount of work is done by the field, the potential energy of the charge field system is changed by an amount du=-q 0 E. ds. For a finite displacement of the charge from point A to point B, the change in potential energy of the system ΔU = U B - U A is

3 Potential Difference and Electric Potential

4 Potential Difference and Electric Potential

5 Potential Difference and Electric Potential

6 Potential Differences in a Uniform Electric Field Let us calculate the potential difference between two points A and B separated by a distance IsI = d, where s is parallel to the field lines. Then Two points in an electric field.

7 Potential Differences in a Uniform Electric Field The negative sign indicates that the electric potential at point B is lower than at point A; that is, V B < V A. Electric field lines always point in the direction of decreasing electric potential, as shown in the Figure below. (a) When the electric field E is directed downward, point B is at a lower electric potential than point A. When a positive test charge moves from point A to point B, the charge field system loses electric potential energy. (b) When an object of mass m moves downward in the direction of the gravitational field g, the object field system loses gravitational potential energy.

Potential Differences in a Uniform Electric Field A uniform electric field directed along the positive x axis. Point B is at a lower electric potential than point A.

8 Potential Differences in a Uniform Electric Field A uniform electric field directed along the positive x axis. Point B is at a lower electric potential than point A. Points B and C are at the same electric potential. A system consisting of a positive charge and an electric field loses electric potential energy when the charge moves in the direction of the field. As the charged particle gains kinetic energy, the charge field system loses an equal amount of potential energy. A system consisting of a negative charge and an electric field gains electric potential energy when the charge moves in the direction of the field. The more general case of a charged particle that moves between A and B in a uniform electric field such that the vector s is not parallel to the field lines, gives thus

9 Electric Potential Due to Various Charge Distributions

00) m, (i) Find the total electric potential due to these charges at the point P, whose coordinates are (4.

10 The Electric Potential Due to Two Point Charges Example 1: The Electric Potential Due to Two Point Charges A charge q 1 = 2.00 μ C is located at the origin, and a charge q 2 = μc is located at (0, 3.00) m, (i) Find the total electric potential due to these charges at the point P, whose coordinates are (4.00, 0) m (ii) Find the change in potential energy of the system of two charges plus a charge q 3 = 3.00 μc as the latter charge moves from infinity to point P Solution (i) For two charges,

11 The Electric Potential Due to Two Point (ii) Charges

12 The Millikan Oil-Drop Experiment During the period from 1909 to 1913, Robert Millikan performed a brilliant set of experiments in which he measured e, the magnitude of the elementary charge on an electron, and demonstrated the quantized nature of this charge. His apparatus, diagrammed in the Figure, contains two parallel metallic plates. Oil droplets from an atomizer are allowed to pass through a small hole in the upper plate. Millikan used x-rays to ionize the air in the chamber, so that freed electrons would adhere to the oil drops, giving them a negative charge. A horizontally directed light beam is used to illuminate the oil droplets, which are viewed through a telescope whose long axis is perpendicular to the light beam. When the droplets are viewed in this manner, they appear as shining stars against a dark background, and the rate at which individual drops fall can be determined. Let us assume that a single drop having a mass m and carrying a charge q is being viewed and that its charge is negative. If no electric field is present between the plates, the two forces acting on the charge are the gravitational force mg acting downward and a viscous drag force F D acting upward.

13 The Millikan Oil-Drop Experiment Schematic drawing of the Millikan oil-drop apparatus. The forces acting on a negatively charged oil droplet in the Millikan experiment

14 The Millikan Oil-Drop Experiment Now suppose that a battery connected to the plates sets up an electric field between the plates such that the upper plate is at the higher electric potential. In this case, a third force qe acts on the charged drop. Because q is negative and E is directed downward, this electric force is directed upward, as shown in Figure b. If this force is sufficiently great, the drop moves upward and the drag force F D acts downward. When the upward electric force qe balances the sum of the gravitational force and the downward drag force F D, the drop reaches a new terminal speed ν in the upward direction. With the field turned on, a drop moves slowly upward, typically at rates of hundredths of a centimeter per second. The rate of fall in the absence of a field is comparable. Hence, one can follow a single droplet for hours, alternately rising and falling, by simply turning the electric field on and off. After recording measurements on thousands of droplets, Millikan and his co-workers found that all droplets, to within about 1% precision, had a charge equal to some integer multiple of the elementary charge e :

15 Applications of Electrostatics The practical application of electrostatics is represented by such devices as lightning rods and electrostatic precipitators and by such processes as xerography and the painting of automobiles. Scientific devices based on the principles of electrostatics include electrostatic generators, the field-ion microscope, and ion-drive rocket engines. Assignment 1 With aid a digram describe the Van de Graaff Generator

16 Capacitors

17 Capacitors Capacitors are devices that store electric charge. Capacitors are commonly used in a variety of electric circuits. For instance, they are used to tune the frequency of radio receivers, as filters in power supplies, to eliminate sparking in automobile ignition systems, and as energy-storing devices in electronic flash units. A capacitor consists of two conductors separated by an insulator. The capacitance of a given capacitor depends on its geometry and on the material called a dielectric- that separates the conductors.

18 Capacitors Definition of Capacitance

19 Capacitors Capacitance of a parallel-plate capacitor The capacitance of a parallel-plate capacitor is proportional to the area of its plates and inversely proportional to the plate separation,

20 Capacitors Example: Parallel-Plate Capacitor

shell of negligible thickness, radius b > a, and charge -Q.

21 Capacitors Example: The Cylindrical Capacitor A solid cylindrical conductor of radius a and charge Q is coaxial with a cylindrical shell of negligible thickness, radius b > a, and charge -Q. Find the capacitance of this cylindrical capacitor if its length is l Solution

and charge - Q concentric with a smaller con-ducting sphere of

22 Capacitors Example: The Spherical Capacitor A spherical capacitor consists of a spherical conducting shell of radius b and charge - Q concentric with a smaller con-ducting sphere of radius a and charge Q. Find the capacitance of this device. Solution

23 Capacitors Combinations of Capacitors: Parallel Combination

24 Series Combination Capacitors

25 Capacitors Example: Find the charges on the capacitors in the figure and the potential difference across them

26 Capacitors Example: A Paper-Filled Capacitor i. Find its capacitance ii. What is the maximum charge that can be placed on the capacitor? Solution (i)

27 Capacitors (ii) The dielectric strength of paper is 16 x 10 6 V/m. Because the thickness of the paper is 1.0 mm, the maximum voltage that can be applied before breakdown is

28 Current Electricity Electric Current The current is the rate at which charge flows through this surface. If ΔQ is the amount of charge that passes through this area in a time interval Δt, the average current I av is equal to the charge that passes through A per unit time: The instantaneous current is defined as I dq dt The steady current is defined as I Q t 28

29 Current Electricity Microscopic Model of Current A section of a uniform conductor of cross-sectional area A.

30 Current Electricity Microscopic Model of Current

31 Current Electricity Example : Drift Speed in a Copper Wire

32 Resistance Current Electricity

33 Current Electricity Ohm s law Materials that obey the above equation are said to follow Ohm s law, Ohm s law states that

34 Current Electricity Ohm s law A uniform conductor of length l and cross-sectional area A. A potential difference ΔV=V b -V a maintained across the conductor sets up an electric field E, and this field produces a current I that is proportional to the potential difference. A potential difference ΔV=V b -V a is maintained across the wire, creating in the wire an electric field and a current. If the field is assumed to be uniform, the potential difference is related to the field through the relationship

35 Current Electricity Resistance Resistance has SI units of volts per ampere. One volt per ampere is defined to be one ohm (Ω): The inverse of conductivity is resistivity

36 Current Electricity Example: The Resistance of a Conductor Calculate the resistance of an aluminum cylinder that has a length of 10.0 cm and a cross-sectional area of 2.00 x 10-4 m 2. Repeat the calculation for a cylinder of the same dimensions and made of glass having a resistivity of 3.0 x Ωm. Solution

37 Current Electricity Example : The Resistance of Nichrome Wire (i) Calculate the resistance per unit length of a 22-gauge Nichrome wire, which has a radius of mm. (ii) If a potential difference of 10 V is maintained across a 1.0-m length of the Nichrome wire, what is the current in the wire? Solution (i) The cross-sectional area of this wire is (ii)

Current Electricity Example: The Radial Resistance of a Coaxial Cable Coaxial cables are used extensively for cable television and other electronic applications.

38 Current Electricity Example: The Radial Resistance of a Coaxial Cable Coaxial cables are used extensively for cable television and other electronic applications. A coaxial cable consists of two concentric cylindrical conductors. The region between the conductors is completely filled with silicon, as shown in Figure, and current leakage through the silicon, in the radial direction, is unwanted. The radius of the inner conductor is a " cm, the radius of the outer one is b " 1.75 cm, and the length is L " 15.0 cm. Calculate the resistance of the silicon between the two conductors. Solution

39 Current Electricity Resistance and Temperature Over a limited temperature range, the resistivity of a conductor varies approximately linearly with temperature according to the expression Where ρ is the resistivity at some temperature T (in degrees Celsius), ρ 0 is the resistivity at some reference temperature T 0 (usually taken to be 20 C), and α is the temperature coefficient of resistivity. The temperature coefficient of resistivity can be expressed as

40 Current Electricity Example: A Platinum Resistance Thermometer A resistance thermometer, which measures temperature by measuring the change in resistance of a conductor, is made from platinum and has a resistance of 50.0 Ω at 20.0 C. When immersed in a vessel containing melting indium, its resistance increases to 76.8 Ω. Calculate the melting point of the indium. Solution

Chapter 1 The Electric Force

Chapter 1 The Electric Force 1. Properties of the Electric Charges 1- There are two kinds of the electric charges in the nature, which are positive and negative charges. - The charges of opposite sign