PHY 184 Title: The Electric Field Week1 - Spring 2007 Lecture 4 1/11/07 184 Lecture 4

Clicker registration in lon-capa closes on January 22. Announcements Clicker registration in lon-capa closes on January 22. Helproom schedule: see LON-CAPA Stay after the lecture today for the Honors Option. 1/11/07 184 Lecture 4

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 (+) 1/11/07 184 Lecture 4

E field — QUALITATIVE 1/11/07 184 Lecture 4

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) 1/11/07 184 Lecture 4

The Electric Field (2) 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 q + Test charge: point object with a very small positive charge so that it does not modify the original field 1/11/07 184 Lecture 4

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.” 1/11/07 184 Lecture 4

E field — QUANTITATIVE 1/11/07 184 Lecture 4

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 1/11/07 184 Lecture 4

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: 1/11/07 184 Lecture 4

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!) 1/11/07 184 Lecture 4

Electric Field Lines 1/11/07 184 Lecture 4

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. Unique 1/11/07 184 Lecture 4

Example 1/11/07 184 Lecture 4

Properties of Field Lines 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 Weak Strong 1/11/07 184 Lecture 4

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 1/11/07 184 Lecture 4

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 1/11/07 184 Lecture 4

Determine the direction of E(x) for points on the plane half-way between the charges. 1/11/07 184 Lecture 4

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. 1/11/07 184 Lecture 4

Determine the direction of E(x) for points on the plane half-way between the charges. 1/11/07 184 Lecture 4

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. 1/11/07 184 Lecture 4

Quiz Identify the charges (positive or negative) in the configuration Positive: A, B, C Negative D, E, F A B C D E F 1/11/07 184 Lecture 4

Demo - Electric Field Lines Demo - visualization of electric field lines Coulomb force Grass seeds - + The charge of grass seeds is redistributed by induction. The Coulomb force makes the seeds align along the field lines. 1/11/07 184 Lecture 4

E(x) = F/q (definition) E = sum of Ei (superposition) 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 = q E(x). The electric force is a field effect — not action at a distance. 1/11/07 184 Lecture 4