PHY 184

1. PHY 184 Week1 - Spring 2007 Lecture 4 Title: The Electric Field 184 Lecture 4

2. Announcements • Clicker registration in lon-capa closes on January 22. • Helproom schedule: see LON-CAPA • Stay after the lecture today for the Honors Option. 184 Lecture 4

3. Review - Coulomb’s Law • The electric force F between two charges, q1 and q2, separated by a distance r is given by Coulomb’s Law: • 1/r2 dependence • The constant k is called Coulomb’s constant and is given by Opposite charges: F is attractive (-) Like charges: F is repulsive (+) 184 Lecture 4

4. E field —QUALITATIVE 184 Lecture 4

5. The Electric Field Field Theory The electric force is not “action at a distance” but is the action of a field. A field is a physical entity that extends throughout a volume of space and exerts forces. Electric field = E(x,t) Magnetic field = B(x,t) 184 Lecture 4

6. The Electric Field (2) + + Test charge q • A charge creates an electric field around itself and the other charge feels that field. Electric field at a given point in space: place a positive test charge q at the point and measure the electrostatic force that acts on the test charge; then Test charge: point object with a very small positive charge so that it does not modify the original field 184 Lecture 4

7. The Electric Field (3) • A field is not just an abstract concept that we use to describe forces. The field is real. • The electric field extends throughout space and exerts forces on charged particles. • If we place a positive point charge in an electric field, there will be a vector force on that charge in the direction of the electric field • The magnitude of the force depends on the strength of the electric field. Field theory versus “action at a distance.” 184 Lecture 4

8. E field —QUANTITATIVE 184 Lecture 4

9. Precise Definition of Electric Field • We define the electric field in terms of the force it exerts on a positive point charge • Unit of the electric field: N/C (newtons per coulomb) • We can then write • Note that the electric force is parallel to the electric field and is proportional to the charge • The force on a negative charge will be in the opposite direction 184 Lecture 4

10. Example – Field of a point charge • What is the field created by a point charge q? • Consider a “test charge” q0 at point x. • Force on q0: • Electric field at x: 184 Lecture 4

11. Superposition of Electric Fields • Suppose we have many charges. • The electric field at any point in space will have contributions from all the charges. • The electric field at any point in space is the superposition of the electric field from n charges is • Note that the superposition applies to each component of the field (x, y, z). (vectors!) 184 Lecture 4

12. Electric Field Lines 184 Lecture 4

13. Electric Field Lines Unique • We can represent the electric field graphically by electric field lines— i.e., curves that represent the vector force exerted on a positive test charge. • Electric field lines will originate on positive charges and terminate on negative charges. • Electric field lines do not cross. (Why?) • The electric force at a given point in space is tangent to the electric field line through that point. 184 Lecture 4

14. Example 184 Lecture 4

15. Properties of Field Lines Weak Strong • The strength of the electric field is represented by the density of electric field lines • The direction of the electric field is tangent to the electric field lines 184 Lecture 4

16. Field Lines from a Point Charge • The electric field lines from a point charge extend out radially. • For a positive point charge, the field lines point outward • Terminate at infinity • For a negative charge, the field lines point inward • Originate at infinity 3D 2D 184 Lecture 4

17. Electric Field Lines for Two Point Charges • We can use the superposition principle to calculate the electric field from two point charges. • The field lines will originate from the positive charge and terminate on the negative charge. 2d 3d 184 Lecture 4

18. Determine the direction of E(x) for points on the plane half-way between the charges. 184 Lecture 4

19. Electric Field Lines from Identical Point Charges • The electric field from two identical point charges • For two positive charges, the field lines originate on the positive charges and terminate at infinity. • For two negative charges, the field lines terminate on the negative charges and originate at infinity. 184 Lecture 4

20. Determine the direction of E(x) for points on the plane half-way between the charges. 184 Lecture 4

21. General Observations about Field Lines • If the field lines connect, we have an attractive force • Imagine the charges pulling on each other • If the field lines seem to spread out, we have a repulsive force • Imagine the charges pushing each other apart • Field lines always originate on positive charge and terminate on negative charge. • Field lines never cross. 184 Lecture 4

22. Quiz B A D Positive: A, B, C Negative D, E, F E F C • Identify the charges (positive or negative) in the configuration 184 Lecture 4

23. Demo - Electric Field Lines - Grass seeds Coulomb force + • Demo - visualization of electric field lines The charge of grass seeds is redistributed by induction. The Coulomb force makes the seeds align along the field lines. 184 Lecture 4

24. Summary E(x) = F/q (definition) E = sum of Ei (superposition) The electric force on a charged particle q located at position x is F = qE(x). The electric force is a fieldeffect —not action at a distance. 184 Lecture 4