Physics I Class 19 The Electric Field Rev. 13-Mar-04 GB 19-1 What Is a Field? A field is nothing more than a function of location, either f(X,Y) or f(X,Y,Z). There is a uniquely defined value of a certain quantity at each point. Example – a temperature map: 19-2 Temperature Map (Temperature Field) 19-3 Coulomb’s Law of Electrostatic Force (Review) F 1 q1 q 2 (r̂ ) (Prof. B’s version.) 2 4 0 r The meaning of each term: F: Electrostatic force on charge 1 from charge 2. 1 2 2 : Electrostatic force constant = 8.98755 × 10 +9 N m /C 4 0 q1 : Value of charge 1, positive or negative. q 2 : Value of charge 2, positive or negative. r 2 : Center distance from point charge 1 to point charge 2, squared. r̂ : Unit vector from charge 1 to charge 2. 19-4 Superposition of Electrostatic Forces (Review) +5.0 C +1.0 C Y 1 X resultant -3.0 C N 1 q1 q i Fon 1 ( r̂i ) (find and add X and Y components) 2 i 2 4 0 ri 19-5 The Idea of Electric Field (Step 1) When finding the force on charge #1, we notice that q1 appears in each term in the sum, so we can factor it out of the sum: N N 1 qi 1 q1 q i Fon 1 ( r̂i ) q1 ( r̂i ) 2 2 i 2 4 0 ri i2 4 0 ri Note that the quantity in { } above is a vector. 19-6 The Idea of Electric Field (Step 2) After doing the first problem, suppose we were asked to solve a second problem with a different charge at position #1, call it q1´. If we were smart enough to have saved the vector part from the first problem, we could find the new force just by multiplying by q1´ instead of q1: N N 1 qi 1 q1 q i 1 Fon ( r̂i ) q1 ( r̂i ) 2 2 i 2 4 0 ri i2 4 0 ri 19-7 The Idea of Electric Field (Step 3) The vector quantity we have calculated depends on the location of the point (#1). depends on the unit vectors to the other charges. depends on the distances to the other charges. depends on the values of the other charges. It does not depend on the value of the charge at the point. In fact, it can be calculated even when there is no charge there! Fon1 N 1 qi E(point #1) (r̂i ) Electric Field 2 q1 i 2 4 0 ri Fon 1 q1 E ( point #1) Force / Field Relationship 19-8 The Electric Field of a Point Charge (as a Source) The electric field is a vector field, meaning at each point in space the electric field has a magnitude and a direction. We show that by drawing arrows at representative points in the correct directions with lengths proportional to the magnitudes. Away from positive Toward negative + - Just because we don’t draw an electric field vector at a point doesn’t mean there is no electric field there. 19-9 Example Problem A sphere with mass m and charge +q is suspended in a horizontal electric field, E, by a string. What is the angle that the string makes with the vertical direction? 19-10 Example Problem The Six-Step Method 1. Identify Forces Tension from string. Gravity. Electrostatic. 2. Coordinate System: X right, Y up 3. Free-Body Diagram 4. Resolve Off-Axis Forces 5. Newton’s 2nd Law 6. Solve 19-11 Example Problem Solution X: q E T sin( ) m a x 0 Y: T cos( ) m g m a y 0 T cos( ) m g T sin( ) q E T sin( ) qE tan( ) T cos( ) mg 19-12 Class #19 Take-Away Concepts 1. Electric field from point charge sources: (Total field is the superposition of point source fields.) 1 qi E ( r̂i ) 2 4 0 ri 2. Force on a charge in an electric field: 3. 4. Electric field points away from + source charges. Electric field points toward – source charges. F qE 19-13 Class #19 Problems of the Day ___1. An electron is placed in a region of space where the magnitude of the electric field is 100 N/C and the direction of the electric field is north. The direction of the electric force on the electron is: A. B. C. D. E. North. South. East. West. Undefined unless we know the locations and values of the charges that create the electric field. 19-14 Class #19 Problems of the Day 2. An electron begins the problem traveling north at 5 x 106 m/s in a region of space where the electric field is 100 N/C in the north direction. How far will the electron travel before it comes to a stop momentarily? Or will the electron not come to a momentary stop? Some useful constants: e = 1.6 x 10-19 C me = 9.1 x 10-31 kg 19-15 Activity #19 Electric Fields (Computer Simulation Activity) Objective of the Activity: 1. 2. Think about electric fields. Use the simulation program to draw electric field vectors and field lines. 19-16