Lecture 7 Ch22. Finding the Electric Field – I University Physics: Waves and Electricity Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com The Electric Field The Coulomb’s law tells us how a charged particle interacts with another charged particle. The question now: Since the particles do not touch, how can one particle push or pull the other? How can there be such an action at a distance with no visible connection between the particles? The concept of Electric Field is introduced to explain this question. Erwin Sitompul University Physics: Wave and Electricity 7/2 The Electric Field The electric field is a vector field. It consists of a distribution of vectors, one for each point in the region around a charged object. We can define the electric field at some point, such at point P, by placing a positive charge q0, called a test charge. → We then measure the electrostatic force F that acts on the test charge. → The electric field E at point P is defined as: F E q0 • The direction of force defines the direction of field Erwin Sitompul University Physics: Wave and Electricity 7/3 The Electric Field The positive test charge q0 does not “see” the charged object. Instead, it “feels” the electric field produced by the charged object and gives response. The SI unit for the electric field is the newton per coulomb (N/C). Note: The field at point P existed both before and after the test charge was put there. Here, we assume that the presence of the test charge does not affect the charge distribution on the charged object. Erwin Sitompul University Physics: Wave and Electricity 7/4 Electric Field Lines In order to understand it better, we will try to visualize the electric field now. Michael Faraday introduced the idea of electric fields in the 19th century and thought of the space around a charged body as filled with electric field lines . The direction of the field lines indicate the direction of the electric force acting on a positive test charge. The density of the field lines is proportional to the magnitude of the field. • The field strength is related to the number of lines that cross a certain unit area perpendicular to the field Erwin Sitompul University Physics: Wave and Electricity 7/5 Electric Field Lines The figure shows a positive test charge, placed near a sphere of uniform negative charge. The electrostatic force points toward the center of the sphere. The electric field vectors at all points are directed radially toward the sphere. The spreading of the field lines with distance from the sphere tells us that the magnitude of the electric field (field strength) decreases with distance from the sphere. Erwin Sitompul University Physics: Wave and Electricity 7/6 Electric Field Lines Electric field lines extend away from positive charge (where they originate) and toward negative charge (where they terminate). Erwin Sitompul University Physics: Wave and Electricity 7/7 Electric Field Lines The figure below shows an infinitely large, nonconducting sheet (or plane) with a uniform distribution of positive charge on one side. Due to symmetry, some forces will cancel one another. The net electrostatic force on the positive test charge will be perpendicular to the sheet and point away from it. Erwin Sitompul University Physics: Wave and Electricity 7/8 The Electric Field Due to a Point Charge From Coulomb’s law, the electrostatic force due to q1, acting on a positive test charge q0 is: F0 k q0 q1 r10 rˆ 2 10 The electric field due to a point charge q1 is: F0 q1 E0 k rˆ 2 10 q0 r10 The field of a positive point charge is shown on the right, in vector form. The magnitude of the field depends only on the distance between the point charge (as the field source) and the location where the field is measured. Erwin Sitompul University Physics: Wave and Electricity 7/9 The Electric Field Due to a Point Charge Electric field is a vector quantity. Thus, the net, or resultant, electric field due to more than one point charge is the superposition of the field due to each charge. The net electric field at the position of the test charge, due to n point charges, is: E0,net E01 E02 E03 q1 k r10 n E0,net k m 1 Erwin Sitompul rˆ k 2 10 qm rm 0 q2 r20 E0n rˆ k 2 20 q3 r30 rˆ 2 30 k qn rn0 rˆ 2 n rˆ 2 m0 University Physics: Wave and Electricity 7/10 Checkpoint The figure below shows a proton p and an electron e on an x axis. What is the direction of the electric field due to the electron at: Rightward (a) Point S? Leftward (b) Point R? What is the direction of the net electric field at Leftward (c) Point R? Rightward (d) Point S? • p and e have the same charge magnitude • R and S are closer to e than to p. Erwin Sitompul University Physics: Wave and Electricity 7/11 Example I A point → source q1 = 20 nC is located at S(1,4). Find the electric field E at P(5,1). All units are in SI. rS ˆi 4jˆ r 5iˆ ˆj ˆ 4iˆ 3jˆ rSP rP rS (5iˆ ˆj) (iˆ 4j) rSP (4) 2 (3) 2 5 rSP 4iˆ 3jˆ rˆSP 0.8iˆ 0.6jˆ rSP 5 P • Field at the measurement point • Source charge E0 k q1 r10 rˆ 2 10 EP k qS rSP rˆ 2 SP 9 (20 10 ) ˆ 8.99 109 (0.8iˆ 0.6j) 2 (5) 5.754iˆ 4.315jˆ V m • Vector pointing from source charge to measurement point Erwin Sitompul University Physics: Wave and Electricity 7/12 Example II A point source q1 = 20 nC is located at S(1,4). Determine some points near S, where the magnitude of the electric field E is equal to 30 V/m. EP k EP k EP k qS rSP rˆ 2 SP qS rSP 2 rˆSP E E • The magnitude of a vector is the scalar value of the vector itself rˆ 1 qS rSP 2 (20 10 9 ) 30 8.99 10 rSP 2 9 • The magnitude of a unit vector always equals 1 (20 109 ) rSP 8.99 10 30 rSP 2.448 • The points near S must 2 9 be 2.448 m away from S • Where are they? Erwin Sitompul University Physics: Wave and Electricity 7/13 Example II y • Location of points where the magnitude of E is equal to 30 V/m P2 q1 P3 4 + Some points near S with E = 30 V/m are: P1(3.448,4) P2(1,6.448) P3(–1.448,4) P4(1,1.552) P1 r = 2.448 P4 1 Erwin Sitompul x University Physics: Wave and Electricity 7/14 Checkpoint The figure here shows four situation in which charged particles are at equal distances from the origin. Rank the situations according to the magnitude of the net electric field at the origin, greatest first. All the same • Be sure to know how and why Erwin Sitompul University Physics: Wave and Electricity 7/15 Application: Ink-Jet Printing Ink-jet printer is an invention to meet the need for high-quality, high-speed printing. The figure below shows a negatively charged ink drop moving between two→ conducting plate. A uniform downward-directed electric field E has been set up. The drop is deflected upward and then strikes the→paper at a position that is determined by the magnitudes of E and the charge q of the drop. Erwin Sitompul University Physics: Wave and Electricity 7/16 Homework 6: Three Particles Three particles are fixed in place and have charges q1 = q2 = +p and q3 = +2p. Distance a = 6 μm. What are the magnitude and direction of the net electric field at point P due to the particles? p 1.602 1019 C e 1.602 1019 C Erwin Sitompul University Physics: Wave and Electricity 7/17 Homework 6: Three Particles New The figure below shows two charged particles on an x axis, –q –3.2×10–19 C at x –3 m and q 3.2×10–19 C at x 3 m. What are the (a) magnitude and (b) direction of the net electric field produced at point P at y 4 m? Erwin Sitompul University Physics: Wave and Electricity 7/18