Outline. Part 1, Topic 2 Electric Fields. Dr. Sven Achenbach - based on a script by Dr. Eric Salt - Particles of Matter. Topic 2: Electric Fields

Transcription

1 : PHYS 155 (Part 1, Topic 2) Handouts p. 1 Outline slide # University of Saskatchewan Undergraduate Course Phys 155 Introduction to Electricity and Magnetism Part 1, Topic 2 Electric Fields Dr. Sven Achenbach - based on a script by Dr. Eric Salt - Phys : Electric Fields 3 Topic 2: Electric Fields Particles of Matter Introductory Remarks topic 2 deals with how electric fields are used to determine forces and work done it is a general introduction & link to your high school physics education, not covered by our text book (Cutnell & Johnson) topic does not cover how electric fields are created refer to subsequent topic 3, which is covered by the text book, and also develops equations to give exact forces for a certain electric field a few definitions from topic 2 will be repeated in topic 3 Fundamental Particles 3 fundamental particles of an atom - electron - proton - neutron they have intrinsic properties of - mass - charge Phys : Electric Fields 2 Phys : Electric Fields 4

2 : PHYS 155 (Part 1, Topic 2) Handouts p. 2 Particles of Matter Charge 2 types of charge - negative (charge intrinsic to an electron) - positive (charge intrinsic to a proton) base unit of charge is Coulomb C this is the charge on about electrons or protons 1 electron or 1 proton carry the smallest amounts of (neg. or pos.) net charge they have the same magnitude (just the sign differs) - charge on 1 electron is denoted e or e - - charge on 1 proton is denoted e or +e or e e C C Phys : Electric Fields 5 Phys : Electric Fields 7 Particles of Matter Electric Fields Intrinsic Properties Force an electric field is a force field particle charge [C] mass [g] radius [m] the force acts on the intrinsic property of charge electron proton neutron none the force exerted by the field is proportional to the excess charge (net charge) on the (test) object (an object has excess charge if it has more (or fewer) electrons than protons) the force [in Newtons N] per unit charge [in Coulombs C] is denoted E [in units of N/C] the force lines of a map of an electric field are called E lines or electric field lines the arrows on the field lines indicate the direction of force the field exerts on a positive charge Phys : Electric Fields 6 Phys : Electric Fields 8

3 : PHYS 155 (Part 1, Topic 2) Handouts p. 3 Electric Fields Example 1 A particle located at point A has an excess (net) charge of +19 C. What is the magnitude of the force on that particle? Is the direction of the force down & to the left or up & to the right? Phys : Electric Fields 9 Phys : Electric Fields 11 Electric Fields Energy Contours (Equipotential Surfaces) x value of E in direction of x-axis Notation E is a 3-dimensional vector [in units N/C] that is a function of position in general, E at a point (x,y,z) is expressed as v E x, y, z = E x, y, z iˆ + E x, y, z ˆj + E ( ) ( ) ( ) ( x, y, z)kˆ at point (x,y,z) y times unit vector in x-direction or without giving the coordinates for the point E (x,y,z) = E (x,y,z) is called the electric field strength at point (x,y,z) z v E = E iˆ + E ˆj + E kˆ x y z of an Electric Field energy contours on a map of an electric field are called equipotential surfaces (lines) equi... from latin: aequus: same (or here: constant) along an equipotential surface (line), the value remains the same / constant from equipotential surface (line) to surface (line) the value changes value associated with equipotential surfaces (lines) is called electric potential energy (or short electric potential or,potential ) [in units Joules/Coulombs J/C] 3D 2D the field strength at a point A labeled on a map is often written as E or E A Phys : Electric Fields 10 Phys : Electric Fields 12

4 : PHYS 155 (Part 1, Topic 2) Handouts p. 4 Energy Contours (Equipotential Surfaces) Energy Contours (Equipotential Surfaces) 1) What is the electric potential of point A? 2) What is the electric potential of point B? 3) What is the electric potential of point A with respect to point B? 4) How much work is required to move a positively charged particle with an excess charge of +23 C from point A to point B? 5) How much work is required to move a positively charged particle with a net charge of +11 C from point D to point A? Example 2 Phys : Electric Fields 13 Example 3 1) What is the average force per unit charge exerted by the field on a charged object moved from A to B along the electric field line that links them? The straight line distance from A to B is measured to be 0.4 m. Note: result for assumption of positively charged object this negative value (-2.5 N / C ) states that the mover exerts a force in opposite direction of the movement (definition of work) the force exerted by the mover is opposite to the force exerted by the field (upstream) force exerted by the field is +2.5 N / C in the direction of the motion (which is in the direction of the field lines ) Phys : Electric Fields 15 Energy Contours (Equipotential Surfaces) Example 3 1) What is the average force per unit charge exerted by the field on a charged object moved from A to B along the electric field line that links them? The straight line distance from A to B is measured to be 0.4 m. 2) What is the average tangential component of the force exerted by the field on a charged object if the object is moved along curve S from point C to D, and curve S is 2 m long? Phys : Electric Fields 14 Phys : Electric Fields 16

5 : PHYS 155 (Part 1, Topic 2) Handouts p. 5 Energy stored in Electric Fields Moving Charges whenever a mover does positive work by moving charge in space (in an electric field), the energy of the electric field increases e.g. - moving a pos. charge from lower to higher potential pos. work done energy of electric field increases - neg. lower to higher work given off decreases - pos. higher to lower work given off decreases - neg. higher to lower pos. work done increases of an Electric Field knowing the electric potential between 2 points in an electric circuit is key to the analysis of that circuit the electric potential is always measured between 2 points the variable (symbol) for the electric potential is V Note: sometimes, the variable is referred to as U instead of V) the variable V AB is used to represent the electric potential between points B and A, referred to as electric potential (or voltage) at point A with respect to point B by definition, the work W required to move an object with a net charge Q from point B to point A is unit of the electric potential (derived from Joules/Coulombs J/C) is a Volt V this is why the electric potential is also referred to as voltage W V AB = Q Note: the symbol V is used for both, variable representing the electric potential and its abbreviated unit Volts. Sometimes, the variable is written in italic font or replaced by U. Otherwise, they are distinguished by context. Phys : Electric Fields 17 Phys : Electric Fields 19 Example 4 1) An object with a net positive charge of 7 C is moved from point A to point B. To do this, the mover does 21 J of work. What is the electric potential at point B with respect to point A (i.e., what is V BA )? 2) What is the potential energy of an object at point B with respect to point A if that object is positively charged with +2 C of charge? Phys : Electric Fields 18 Phys : Electric Fields 20

6 : PHYS 155 (Part 1, Topic 2) Handouts p. 6 Example 5 Points G and H are 2 points in space where an electric field is present. V HG = 10 V. How much work is required to move +19 C of charge from point G to H? Example 7 1) What is the direction of the electric field? 2) What are V AB and V BA? 3) What is V CD? 4) How much work is required to move -29 C of charge from point D to point A? 5) What is the strength of the electric field at H if dx = 1 m? Phys : Electric Fields 21 Phys : Electric Fields 23 Example 6 Points G and H are 2 points in space where an electric field is present. V HG = 10 V. How much work is required to move -19 C of charge from point G to H? Phys : Electric Fields 22 Phys : Electric Fields 24

7 : PHYS 155 (Part 1, Topic 2) Handouts p. 7 Relationship between E and V suppose points A and B are on the same electric field line and are a distance Δx apart to move a particle with excess charge Q from points B to A, the mover must exert an average force F ave in the direction of the movement with the general definition of work (or energy) W = F Δx, and work W to be done by a mover to move the particle from B to A (F ave is positive, if its direction is from B to A) 1 W division by Q: F Q = 1 Q F ave W ave Δx Q Q 1 Fave VAB = = Δx Q Δx the mover exerts the force F ave against the field force (and the related electric field E ave ) with field E = force per unit charge [N/C] as defined earlier, and with the neg. sign as above, Moving a Charge in a Field F Q ave = E ave Note: equation justifies that units of electric field N/C are also V/m: Phys : Electric Fields 25 V m F ave E ave W = Δ x VAB = Δx J Nm C N = C = = m m C Phys : Electric Fields 27 Relationship between E and V Electron Volt Δx dx Definition for now, denote V AB as ΔV electric field strength of the electric field was derived to be now, decrease Δx: ΔV Δx dv dx field strength will be the same at points A and B and all points inbetween: E remains constant for extremely small distances Δx dx electric field strength is given by dv E = dx E ave ΔV = Δx an electron volt is denoted ev magnitude of work (or energy) required to move the charge of one electron or proton (e = C) between 2 points that have a difference in electric potential of V = 1 V 1 ev = (1 V) (e) = (1 V) ( C) = VC = J reciprocally, using the definition of ev, the charge on 1 proton is e = (1 ev) / (1 V) = 1 e Phys : Electric Fields 26 Phys : Electric Fields 28

8 : PHYS 155 (Part 1, Topic 2) Handouts p. 8 Electron Volt Example 8 An electron is moved from point A to point B in an electric field where V BA = -7 V. 1) Is the work done by the mover positive or negative? 2) How much energy (in units of Joules) is transfered from the mover to the field? 3) How much energy (in units of ev) is transfered from the mover to the field? Phys : Electric Fields 29