PHYS219; Fall Semester 2014 Lecture 03: Electric Fields Dimitrios GIANNIOS Purdue University
Practical issues No Class next Monday (Labor’s Day) First Homework assignment due next Friday
CHiP in general Due on Fridays before Recitation (10:30am) (50% credit for homework done up to 24 hours later)
Electric field E Both gravity and electrostatic forces are non-contact forces. They act on objects that are not touching each other. The concept of a force field was developed to better describe this action-at-a-distance feature of these forces. Gravitational Field Electric Field
Electric field considerations Electric field is a property of space around charges: it is there all the time! CANNOT depend on the charge qtest one uses to measure it electric force alone FE is NOT a good measure of electric field! suppose you want to define the electric field at distance r away from charge Q: 2FE FE + r 2qtest qtest Q Units E[N/C]
Electric field The presence of a charge produces an electric field Shown by the arrows in the figure A positive charge produces field lines that radiate outward For a negative charge the field lines are directed inward, toward the charge The electric field is a vector and denoted by
Electric field and test charge Consider a point in space where the electric field is If a charge q is placed at the point, the force is given by The charge q is called a test charge By measuring the force on the test charge, the magnitude and direction of the electric field can be inferred
Electric field, cont. The electric force is either parallel or antiparallel to the electric field Parallel if q is positive and antiparallel if q is negative SI units of the electric field are N/C Coulomb’s Law can be used to find the magnitude of the electric field, where Q is the charge producing the field and q is the test charge
Why bother introducing the Electric Field? An electric field is property of space: it is present even when there is no second (or test) charge present to experience the electric force The electric field helps explain how the Coulomb force can act between two charges that are separated by large distances The electric field is essential for understanding electromagnetic waves
Electric Field Lines We visualize an electric field is with electric field lines Field lines are a set of continuous lines that are always parallel to the electric field
Drawing Electric Field Lines Field lines must always begin on positive charges Field lines must always end on negative charges
Drawing Electric Field Lines (more) The Larger the charge the more lines start/end there QA < QB < QC
Another Example: 3 charges Field lines must always begin on positive charges Field lines must always end on negative charges The density electric field lines shows field strength low field, weak force --lines further apart q1 = q3 = q2/2 + + strong field, force --lines close together
software to visualize Electric fields http://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html
Quiz time: where are the charges? Are there more negative or positive charges? How many charges are there? How many positive charges? How many negative charges?
Electric Fields and Multiple Charges To find the electric field due to multiple charges use the principle of superposition Find the electric fields due to each charge Add them as vectors
Example: E produced by 3 charges θ1 θ3 θ2
Example: Analyze its charge separately
Final Answer
The origin of Inverse Square Laws The force between two point charges falls off as 1/r2 Where r is the separation between the charges The electric field also falls off as 1/r2 The electric force also obeys an inverse square law The charged particle “sets up” field lines in its neighborhood The density of the field lines is proportional to the amount of charge on the particle
Inverse Square Laws, cont. The electric field lines emanate outward from a point charge They intercept larger and larger surface areas The surfaces are spherical Their areas increase as A r2 The number of field lines per unit area falls as 1/r2 r