12/15/2015. Newton per Coulomb N/C. vector. A model of the mechanism for electrostatic interactions. The Electric Field

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1 Chapter 15 Lecture The Electric Field A model of the mechanism for electrostatic interactions A model for electric interactions, suggested by Michael Faraday, involves some sort of electric disturbance in the region surrounding a charged object. Physicists call this electric disturbance an electric field. GRAVITATIONAL FORCE vs. ELECTROSTATCS FORCE OBJECT WITH MASS GRAVITATIONAL FORCE vs. ELECTROSTATCS FORCE OBJECT WITH MASS ELECTRIC FIELD PHYSICAL QUANTITY: ELECTRIC FIELD Q Electric field is a property of a location in space that measures the force per unit charge that a charged object would feel if placed at that location. Symbol Units Units symbol Type of PQ E Newton per Coulomb N/C vector 1

2 Your diaper, your field!! ELECTRIC FIELD DUE TO A SINGLE POINTLIKE CHARGED OBJECT ELECTRIC FIELD DUE TO A SINGLE POINT LIKE CHARGED OBJECT We can interpret this field as follows: ELECTRIC FIELD DUE TO A SINGLE POINT LIKE CHARGED OBJECT 1. What is the strength and direction of the electric field 0.4 m away from a 9.0 C electric charge? The E field vector at any location points away from the object creating the field if Q is positive, and toward the object creating the field if Q is negative. 2. At what distance from a 5.5 C electric charge would the electric field strength be 1.90x10 5 N/C? 3. A, B, & C are random points around a 2 C electric charge. Somebody else s diaper, somebody else s field! Find the intensity of the electric field produced by the electric charge at points A, B, & C. Assume each box to be d = 0.1 m C A 2 C B 2

3 ELECTRIC FIELD FELT BY AN ELECTRIC CHARGE ELECTRIC FIELD FELT BY AN ELECTRIC CHARGE INSIDE A UNIFORM EFIELD A 5 C electric charge is placed inside a uniform electric field. F q = k q A q B d 2 a. If an electric force of 0.07 N is exerted on the electric charge, what is the magnitude of the electric field? b. What electric force would be exerted if charge A is substituted by an electric charge of 4 C? E= q F q c. What would the magnitude of a new electric charge be, if an electric force of N is exerted on it? q A E ELECTRIC FIELD LINES (EField Lines) EField lines are a graphic representation of electric fields used by physicists to study and analyze electric fields. Experiment: Grass seeds placed near a charged object. Observation: Grass seed aligned in a specific pattern of lines surrounding the charged object. Electric Field lines point in the direction of the electric field. Electric field lines do not exist but they are useful when analyzing electric fields. ELECTRIC FIELD LINES ELECTRIC FIELD LINES q 2q PROPERTY 1 Efield lines start (leave) on positive charges. Efield lines end (enter) on negative charges. PROPERTY 2 The number of electric field lines is proportional to the magnitude of the charge. The bigger the magnitude of the electric charge the more the amount of Efield lines. 3

4 ELECTRIC FIELD LINES E field lines PROPERTY 3 EField lines will NOT cross each other ELECTRIC FIELD LINES ELECTRIC FIELD LINES Grass seeds in an insulating liquid align with a similar electric field produced by two oppositely charged objects Grass seeds in an insulating liquid align with a similar electric field produced by two objects with the same charge PROPERTIES In which direction would the electric field be at each point? A B C D 4

5 In which direction would the electric field be at each point? d Q Q E = 0 What is the magnitude and direction of the electric field at X? Q d/2 d/2 Q Each charged particle contributes an amount k Q ( d 2 )2 to the field at the center. USING THE SUPERPOSITION PRINCIPLE Draw E field lines for a large, uniformly charged plate of glass at a random point in front of the plate. Using some vector addition gives us the net result E = 8kQ d 2 to the right 5

6 ELECTRIC FIELD USING THE SUPERPOSITION PRINCIPLE 1. Draw the direction of the electric field created by charge Q at point P. 2. Draw the direction of the electric field created by charge q at point P. 3. Draw the direction of the Net Electric field at point P. ELECTRIC FIELD USING THE SUPERPOSITION PRINCIPLE 1. Draw the direction of the Net Electric field at point P. 2. Find the magnitude of the electric field at point P. 1 box = 0.1 m q = 4µC ELECTRIC FIELD USING THE SUPERPOSITION PRINCIPLE 1. Draw the direction of the Net Electric field at point P. 2. Find the magnitude of the electric field at point P. ELECTRIC FIELD USING THE SUPERPOSITION PRINCIPLE 1. Draw the direction of the Net Electric field at point P. 2. Write an expression for the magnitude of the electric field at point P. 1 box = 0.1 m q A = 4µC q B = 4µC 1. Draw the direction of the Electric field between two parallel charged plates.. CONSTANT ELECTRIC FIELDS Draw the path that a negatively charged particle will follow through the parallel charged plates. 6

7 ELECTRIC FIELD DEFLECTS AN INK BALL Draw a force diagram (see picture next slide) Find the magnitude of all forces exerted on the ink ball. Find the time it takes the ink ball to go through the parallel plates. Find the vertical acceleration of the ink ball. Find the vertical displacement the ink ball is deflected so that it lands at a particular spot on a piece of paper. THE V FIELD Can we describe electric fields using the concepts of work and energy? MATHEMATICAL MODELS (FOR ELECTRIC FORCE AND ELECTRIC POTENTIAL ENERGY USE Q & q) ELECTRIC FORCE Divide electric force by q ELECTRIC FIELD 1 ELECTRIC FIELD 2 To do so, we need to describe the electric field not as a forcerelated E field, but as an energyrelated field. ELECTRIC POTENTIAL ENERGY Divide electric potential energy by q ELECTRIC POTENTIAL 1 ELECTRIC POTENTIAL 2 ELECTRIC POTENTIAL Q Symbol PHYSICAL QUANTITY: ELECTRIC POTENTIAL V Electric potential is a property of a location in space that measures the energy per unit charge that a charged object would feel if placed at that location. Units Units symbol Type of PQ Joules per Coulomb (Volts) J/C [ v ] scalar 7

8 THE V FIELD THE V FIELD Both the V field and the E field at a specific location are independent of a test charge and characterize the properties of space at that location. Efield is a vector physical quantity. Direction depends on the type of charge. Vfield is a scalar physical quantity. It can have a negative or positive value depending on the sign of the electric charge Q of the object that creates the field at a particular location Potential difference V Particles in a potential difference The value of the electric potential depends on the choice of zero level, so we often use the difference in electric potential between two points. The Electric Potential Difference V between two points A and B is equal to the difference in the values of electric potential at those points. A positively charged object accelerates from regions of higher electric potential toward regions of lower potential (like an object falling to lower elevation in Earth's gravitational field). A negatively charged particle tends to do the opposite, accelerating from regions of lower potential toward regions of higher potential. V = V B V A ELECTRIC POTENTIAL A, B, & C are random points around a 2 C electric charge. Find the electric potential produced by the electric charge at points A, B, & C. Two 3µC charged point like objects are separated by 0.2 m. Determine the electric potential at a point: A. halfway between the objects Assume each box to be d = 0.1 m C A 2 C B B. 0.2 m to the to the side of one of the objects. 8

9 Suppose that the heart's dipole charges Q and Q are separated by distance d. Write an expression for the V field due to both charges at point A, a distance d to the right of the Q charge. Four objects with the same charge q are placed at the corners of a square of side d. A. Sketch the situation. Identify the center of the square. B. Determine the value of the Electric Field at a point that is located in the center of the square (sketch). C. Determine the value of the Electric Potential at a point that is located in the center of the square. See picture on next slide. Inside an Xray machine is a wire (called a filament) that, when hot, ejects electrons. Imagine one of those electrons, now located outside the wire. It starts at rest and accelerates through a region where the V field increases by 40,000 V. The electron stops abruptly when it hits a piece of tungsten at the other side of the region, producing Xrays. How fast is the electron moving just before it reaches the tungsten? THE VFIELD Equipotential surfaces: Representing the V field The lines represent surfaces of constant electric potential V, called equipotential surfaces. The surfaces are spheres (they look like circles on a twodimensional page). 9

10 Equipotential surfaces: Representing the V field Equipotential surfaces and E field Contour maps: An analogy for equipotential surfaces RELATING THE VFIELD AND THE EFIELD Deriving a relation between the E field and ΔV Deriving a relation between the E field and ΔV We attach a small object with charge q to the end of a very thin wooden stick and place the charged object and stick in the electric field produced by the plate. Draw a Force Diagram Charge is the system Ignore force that Earth exerts on the charge. Charge is not accelerating 10

11 Deriving a relation between the E field and ΔV The stick moves away from the positively charged plate. System is charge and electric field. Draw a force diagram. Draw a workenergy bar chart Deriving a relation between the E field and ΔV Applying the generalized workenergy equation, we get: Equivalently, the component of the E field along the line connecting two points on the xaxis is the negative change of the V field divided by the distance between those two points: E x = V x Ben brings a grounded metal sphere with a wooden handle near a Van De Graaff generator so that their potential is 450,000 v and the sphere does not get charged. Ben pulls the sphere away. Predict the magnitude of the electric field when you see a spark. Deriving a relation between the E field and ΔV The direction of the Efield points direction of decreasing Vfield. in the The relation between the Efield and the Efield tells us: When Vfield is constant, Efield is zero. Two points at a different potential, the closer the points are, the stronger the Efiled will be. Look at the two situation below (point P is located halfway between both charges): Find Magnitude and direction of electric field at point P. Find magnitude of electric potential at point P. Conclusions? CONDUCTORS IN ELECTRIC FIELDS 11

12 Electric field of a charged conductor Electric field of a charged conductor Electric field outside a charged conductor Electric field inside/outside a charged conductor Electric field is a vector physical quantity. Electric field inside the charged conductor cancel each other out. E=0 inside the conductor Electric potential inside/outside a charged conductor Electric Potential is a scalar physical quantity. Electric potential inside the charged conductor add up. V>0 inside the conductor Grounding discharges an object made of conducting material by connecting it to Earth. Electrons will move between and within the spheres until the V field on the surfaces of and within both spheres achieves the same value. Grounding 12

13 Uncharged conductor in an electric field: Shielding The free electrons inside the object become redistributed due to electric forces, until the E field within the conducting object is reduced to zero. Uncharged conductor in an electric field: Shielding The interior is protected from the external field an effect called shielding. Dielectric materials in an electric field DIELECTRICS IN ELECTRIC FIELDS If an atom in a dielectric material resides in a region with an external electric field, the nucleus and the electrons are displaced slightly in opposite directions until the force that the field exerts on each of them is balanced by the force they exert on each other. Polar water molecules in an external electric field Some molecules, such as water, are natural electric dipoles even when the external E field is zero. E field inside a dielectric A dielectric material cannot completely shield its interior from an external electric field, but it does decrease the field. 13

14 E field inside a dielectric Physicists use a physical quantity to characterize the ability of dielectrics to decrease the E field: Dielectric constants for different types of materials The dielectric constant κ Electric force and dielectrics Salt dissolves in blood but not in air The force that object 1 exerts on object 2 is reduced by κ compared with the force it would exert in a vacuum. Inside the dielectric material, Coulomb's law is now written as: When salt is placed in water or blood: Many more collisions occur between molecules than between molecules and air; these can break an ion free from the crystal. Any ions that become separated do not exert nearly as strong as an attractive force on each other because of the dielectric effect. The random kinetic energy of the liquid is sufficient to keep the sodium and chlorine ions from recombining, allowing the nervous system to use the freed sodium ions to transmit information. Tip CAPACITORS 14

15 CAPACITORS A capacitor consists of two conducting surfaces separated by a nonconducting material. The role of a capacitor is to store electric potential energy. BATTERY CAPACITORS A negatively charged particle accelerates from regions of lower potential toward regions of higher potential (more negative electric potential). Charges will stop moving when the V of the battery is the same V of the capacitor. This process happens very quickly. Capacitor in the process of charging Charged capacitor Capacitors (Cont'd) BATTERY BATTERY BATTERY CAPACITANCE When a capacitor is connected to an electric potential difference, the two plates become charged one plate acquires negative charge and the other plate positive charge. The amount of charge acquired by each plate is: CAPACITANCE The proportionality constant C in this equation is called the capacitance of the capacitor. C = q V The unit of capacitance is 1 coulomb/volt = 1 farad (in honor of Michael Faraday). 15

16 the ability of a conductor to Definition: store energy in the form of electrically separated charges. Symbol: PHYSICAL QUANTITY: CAPACITANCE C Units: Farads (F) C q V Capacitors If we consider the capacitor plates to be large flat conductors, charge should be distributed evenly on the plates. The magnitude of the E field between the plates relates to the potential difference from one plate to the other and the distance separating them To double the E field, the charge on other plates has to double. Type of PQ: Scalar QUANTITIES THAT AFFECT THE CAPACITANCE OF A CAPACITOR: PLATE AREA A capacitor with largersurfacearea plates should be able to maintain more charge separation because there is more room for the charge to spread out. QUANTITIES THAT AFFECT THE CAPACITANCE OF A CAPACITOR: DISTANCE SEPARATION A larger distance between the plates leads to a smallermagnitude E field between the plates. Because the magnitude of this E field is proportional to the amount of electric charge on the plates, a larger plate separation leads to a smallermagnitude electric charge on the plates. QUANTITIES THAT AFFECT THE CAPACITANCE OF A CAPACITOR: DIELECTRIC CONSTANT Material between the plates with a large dielectric constant becomes polarized by the electric field between the plates. Thus more charge moves onto capacitor plates that are separated by material of high dielectric constant. Capacitance of a capacitor The capacitance of a particular capacitor should increase if the surface area A of the plates increases, decrease if the distance d between them is increased, and increase if the dielectric constant k of the material between them increases: 16

17 Tip ELECTRIC WORK W q v ELECTRIC POTENTIAL ENERGY Uq [ J ] A capacitor besides of storing electric charge, also stores electric potential energy. W = U q U q q V = 2 MATHEMATICAL MODELS CAPACITANCE C = q V ELECTRIC POTENTIAL ENERGY U q q V = 2 Write a mathematical model for Uq in terms of C and V Write a mathematical model for Uq in terms of C and q MATHEMATICAL MODELS MATHEMATICAL MODELS CAPACITANCE C = q V C A 4 kd Write a mathematical model for Efield in terms of q, k,, A. ELECTRIC POTENTIAL ENERGY GAUSS LAW U q q V = C ( V) ( q) Uq = Uq = 2 2 C 17

18 AP2 EQUATION TABLE TEXTBOOK Estimate the capacitance of your physics textbook, assuming that the front and back covers (area A = m 2, separation d = m) are made of a conducting material. The dielectric constant of paper is approximately 6.0. Determine what the potential difference must be across the covers for the textbook to have a charge separation of 10 6 C (one plate has charge 10 6 C and the other has charge 10 6 C). POINT LIKE CHARGES CAPACITORS Uq = q v 18