How Do We Describe the Electric Field Between Parallel Plates? A REGENTS PHYSICS PRESENTATION BY Mr. Julio Rodriguez

Physics is Life2 © To review the electrostatic field around point charges © To review how to calculate the electric field intensity of a point charge. © To review the forces between between charges as calculated by Coulomb’s Law © Understand the concepts of electric potential difference (“voltage”) and its relationship to electric potential energy. © Calculate the electric field of parallel plate conductors. © Discuss the important features as well as the function of parallel plate conductors OBJECTIVES

Physics is Life3 Electric field is a vector quantity whose direction is defined as the direction which a positive test charge would be pushed when placed in the field. Thus, the electric field direction about a positive source charge is always directed away from the positive source. And the electric field direction about a negative source charge is always directed toward the negative source. What is an Electric Field? + Coming in! Run Away! + Review

Physics is Life4 How Can We Describe the Electric Field Lines Between Two Charges? u Electric field lines for two charges of opposite sign. u Electric field lines for two equal positive charges Review

Physics is Life5 How do We Measure the Strength of Electric Fields? Measuring an electric field is a quite simple process involving a test charge. To measure the strength of an electric field, first a test charge must be placed in its vicinity, then calculate the force the test charge feels. The resulting number is the strength of the electric field. This process is simplified into the following equation In this equation, F is the magnitude of the force, as found by using Coulomb's Law, q is the magnitude of the test charge. The resulting electric strength is measured in Newton’s per a Coulomb (N/C). Review

Physics is Life6  Coulomb's law describes the force between two charged particles. Where Q 1 and Q 2 are the amount of charge and k is a proportionality constant What is Coulomb’s Law? Review

Physics is Life7 Solving Problems Involving The Strength Of An Electric Field Sample Problem A positive charge of 1 x10 -5 C experiences a force of 0.2N when located at a certain point in an electric field. What is the electric field strength at that point? Solution F= 0.2N q=1x10 -5 C E= F/q = 0.2N / 1 x10 -5 C = 2 x 10 4 N/C

Physics is Life 8 Sample problem Find the force between two positive 1.0 C charges when they are 1000m apart? Solution q 1 =q 2 = 1.0 C r = 1000m F = kq 1 q 2 /r 2 where k = 9.0 x 10 9 Nm 2 /C 2 After substitution, F = 9.0 x 10 3 N Solving Problems involving Coulomb’s Law

Physics is Life9 When a Test charge is present in an Electric Field, can it acquire Potential Energy? Can it Acquire Kinetic Energy? + + A charge at any point in an electric field possesses potential energy. Consider the electric field of the positively charged sphere. If we moved a small positive charge +q from B to A, we have to do WORK against the electric field. If we were to “let go” of +q at point A, it will accelerate to B (and beyond) and gain KE. This KE is obtained at the expense of the potential energy (W =  PE) possessed by +q when it was at A. + A B

Physics is Life10 Electric Field & Work of a Small Charge in an Electric Field Consider the motion of the a positive test charge within the electric field created by a positive source charge.

Physics is Life11 Now we will consider the motion of the same positive test charge within the electric field created by a negative source charge. Electric Field & Work of a Small Charge in an Electric Field

Physics is Life12 Complete the following statement: When work is done on a positive test charge by an external force to move it from one location to another, potential energy _________ (increases, decreases). When work is done on a positive test charge to move it from one location to another, potential energy increases. Electric Fields, Work & Electric Potential Energy

Physics is Life13 The following diagrams show an electric field (represented by arrows) and two points - labeled A and B - located within the electric field. A positive test charge is shown at point A. For each diagram, indicate whether work must be done upon the charge to move it from point A to point B. Finally, indicate the point (A or B) with the greatest electric potential energy Work done on charge? Yes or No Electric PE is greatest at: A B Work done on charge? Yes or No Electric PE is greatest at: A B Electric Fields, Work & Electric Potential Energy

Physics is Life14 2. The following diagrams show an electric field (represented by arrows) and two points - labeled A and B - located within the electric field. A positive test charge is shown at point A. For each diagram, indicate whether work must be done upon the charge to move it from point A to point B. Finally, indicate the point (A or B) with the greatest electric potential energy. Work done on charge? Yes or No Electric PE is greatest at: A B Work done on charge? Yes or No Electric PE is greatest at: A B Electric Fields, Work & Electric Potential Energy

Physics is Life15 u Lets look at one of the simplest electric field patterns: the field between *two oppositely charged plates (capacitor). u Supposed a positive test charge is “pushed” from point b to point a. u The work done on the particle is W = Fd or qEd (*F=qE) u When dealing with electrical charges, we like to call this type of energy ELECTRICAL POTENTIAL ENERGY Question: Is there a symbolic relationship with the FORMULA for gravitational potential energy? Electrical Potential Energy

Physics is Life16 Here we see the equation for gravitational potential energy. Instead of gravitational potential energy we are talking about ELECTRIC POTENTIAL ENERGY A charge will be in the field instead of a mass The field will be an ELECTRIC FIELD instead of a gravitational field The displacement is the same in any reference frame and use various symbols Putting it all together! Question: What does the LEFT side of the equation mean in words? The amount of Energy per charge! Electrical Potential Energy vs. Gravitational Potential Energy

Physics is Life17 The amount of energy per charge has a specific name and it is called, VOLTAGE or ELECTRIC POTENTIAL (difference). Why the “difference”? We can therefore write: Electrical Potential Energy Per Charge

Physics is Life18 The difference of potential between two points is defined as the work it takes to move a unit positive charge from the point of lower potential (B) to that at higher potential (A). In this formula, V is the electric potential difference,  PE is the electric potential energy between point b and point a, W is work, and q is the magnitude of the test charge. The SI unit of electric potential difference is Joule/Coulomb or volt (V). Understanding Electric Potential “Difference” For a Charge in an E- Field.

Physics is Life19 Let’s say we have a proton placed between a set of charged plates. If the proton is held fixed at the positive plate, the ELECTRIC FIELD will apply a FORCE on the proton (charge). Since like charges repel, the proton is considered to have a high potential (voltage) similar to being above the ground. It moves towards the negative plate or low potential (voltage). The plates are charged using a battery source where one side is positive and the other is negative. The positive side is at 9V, for example, and the negative side is at 0V. So basically the charge travels through a “change in voltage” much like a falling mass experiences a “change in height. Just like a mass accelerates as it falls, so does the charge in a field of parallel plates. (Note: The electron does the opposite) Understanding Electric Potential “Difference” For Charged Plates Notice the electric field lines at the edges!

Physics is Life20 W is Electric Potential Energy (Joules) is not V is Electric Potential (Joules/Coulomb) a.k.a Voltage, Potential Difference Electric Potential Energy vs. Electric Potential

Physics is Life21 The quantity electric potential is defined as the amount of _____. a. electric potential energy b. force acting upon a charge c. potential energy per charge d. force per charge Answer: C Electric potential is the amount of potential energy per unit of charge. Units of Electric Potential

Physics is Life22 Since the amount of energy per charge is called Electric Potential, or Voltage, the product of the electric field and displacement is also VOLTAGE This makes sense as it is applied usually to a set of PARALLEL PLATES. V=Ed E d V What about the “other side” of the Equation? Notice the electric field lines at the edges!

Physics is Life23 © The work done by the electric field E to move a positive charge q from A to B is W = qV © Using W =Fd and F = qE, the potential difference for a parallel plate conductor is V = Ed © If the potential difference (V) is fixed, the electric field strength is the same (as well as the force on the charge) at any point between the parallel plates. © Internet Link: RegentsPrep.org** Internet Link: RegentsPrep.org** d Important Facts Concerning The Electric Field around Parallel Plates + **Very important!!!

Physics is Life24 Sample Problem It takes 5.0 x J of work to move a positive test charge of 2.5 x C from point X to point Y on an electric field. What is the difference of Potential between X and Y? Solution Work = qV W= 5.0 x J q = +2.5 x C V= W/q = 5.0 x J/2.5 x C = 20 J/C = 20 volts Electric Potential Energy (Work) Between Two Charges

Physics is Life25 Sample Problem A 12-V battery maintains the electric potential difference between two parallel metal plates (capacitor) separated by 0.10m. What is the electric field between the plates? Solution V= 12 V d = 0.10m From V = Ed, we have E = V/d = 12 V/ 0.10m = 1.2 x 10 2 V/m Relation between Electric Potential and Electric Field (Parallel Plates)

Physics is Life26 Relation between Electric Potential and Electric Field (Parallel Plates) Sample problem Two parallel conducting plates (capacitor) are charged to a voltage of 50V. If the separation between the plates is 0.05m, calculate the electric field between them. Solution E= V/d = 50V/0.050m = 1000V/m

u Televisions, Oscilloscopes, Monitors, etc. use an electron beam steered by electric fields to light up the (phosphorescent) screen at specified points E-field metal plates electron beam screen cathode emitter 27 Uses of parallel metal plate conductors in everyday life Why does the beam ocurve toward the positive plate?

Physics is Life28 Other uses of Capacitors A capacitor, sometimes called a condenser, are widely used in electronic circuits: they store charge for later use, as in a camera flash, and energy backup in computers if the power fails; capacitors block surges of charge and energy to protect circuits: very tiny capacitors serve as memory for the “one” and “zeros” of the binary code in the the random access memory (RAM) of computers. Advanced

Physics is Life29 Capacitors can be easily purchased at a local Radio Shack and are commonly found in disposable Kodak Cameras. When a voltage is applied to an empty capacitor, current flows through the capacitor and each side of the capacitor becomes charged. The two sides have equal and opposite charges. When the capacitor is fully charged, the current stops flowing. The collected charge is then ready to be discharged and when you press the flash it discharges very quickly released it in the form of light. Cylindrical Capacitor Advanced Where can we find Capacitors? Can think of something that happens in Nature that simulates a capacitor?

Physics is Life30 Parts of a Capacitor A capacitor consists of two conductors that are close but not touching. A capacitor has the ability to store electric charge. Inside the capacitor, the terminals connect to two metal plates separated by a non- conducting substance, or dielectric. You can easily make a capacitor from two pieces of aluminum foil and a piece of paper. It won't be a particularly good capacitor in terms of its storage capacity, but it will work. dielectric Video: How to make a capacitor Part 1 Video: How to make a capacitor Part 2 Advanced

Physics is Life31 In the picture below, the capacitor is symbolized by a set of parallel lines. Once it's charged, the capacitor has the same voltage as the battery (1.5 volts on the battery means 1.5 volts on the capacitor) The difference between a capacitor and a battery is that a capacitor can dump its entire charge in a tiny fraction of a second, where a battery would take minutes to completely discharge itself. That's why the electronic flash on a camera uses a capacitor -- the battery charges up the flash's capacitor over several seconds, and then the capacitor dumps the full charge into the flash tube almost instantly How do capacitors work? Advanced Internet Link: How Capacitors work YouTube: Capacitor explosion from too much voltage YouTube:How to charge a capacitor Charged capacitor lighting LED

Physics is Life32 Capacitors vs. Batteries In a way, a capacitor is a little like a battery. Although they work in completely different ways, capacitors and batteries both store electrical energy. If you have read How Batteries Work, then you know that a battery has two terminals. Inside the battery, chemical reactions produce electrons on one terminal and absorb electrons on the other terminal. A capacitor is much simpler than a battery, as it can't produce new electrons -- it only stores them.How Batteries Workelectrons Advanced Internet Link: Mechanical Universe: The Electric Battery

Physics is Life33 Summary The change in PE (Work) of a charge q when it moves through a potential difference V is W =qV Potential difference is measured in volts (1V=1J/C) and is sometimes referred to as voltage (V). The electric potential (V) at any point in space is defined as the electric potential energy per unit charge (joules/coulumbs). Electric potential difference (V) is equal to work done to move charge from one point to another divided by the charge. (V = W/q) The potential difference V between two points where a uniform electric field E exists is given by V=Ed

Physics is Life34 What the heck is going on? MIT University LECTURE#1 The Mechanical Universe Video : Potential and Capacitance The Physics Classroom Additional Resources Video Gravitational PE vs Electrical PE