Electric Fields Why electric charges can reach out and touch you.

Learning Objectives Describe the characteristics common to field forces. Describe the characteristics common to electric fields. Describe the forces acting on particles with various charges. Describe the interactions of electric fields from multiple charged objects. Predict how charged particles will act in an electric field. Describe how electric fields create potential energy.

Electric Field Characteristics Field forces radiate out from any source object, surface or particle. –Field forces are projected out into space from a source. –Can act on an object at a distance without actually touching the object. Electric Fields radiate out from a charged source (+ or -) –Field strength is related to the charge magnitude of the source and the distance from the source. –Like charged objects in an electric field are force away from the source, while oppositely charged particles are attracted toward the source. –Produces Field Force lines. Field Force lines move radially away from positive charges and toward negative charges. Field strength is proportional to the number field lines and the distance separating individual lines.

Electric Field Diagrams

Electric Field Interactions When multiple charged objects are brought close together their electric fields interact. –Like charges - Fields repel each other, producing a “neutral” (equilibrium) zone in between. –Opposite charges - Fields combine, with field lines joining. Equal charge - All field lines join Unequal charge - Field lines between particles join, with extra field lines from particle with higher charge radiating outward.

Field Interaction Diagrams

Forces Between 2 Charged Particles Whenever a charged particle is brought into the electric field of a second charged particle electric forces between the 2 particles are created –If the particles have the same charge, the force is repulsive (+) –If the two particles are oppositely charged, the force is attractive (-) –The magnitude of the force is given by “Coulomb’s Law” Coulombs Law – The electrical force existing between two charged particles is related to the charge of the particles and the distance between the particles squared –Formula:F e = k(q 1 q 2 )/r 2 F e – Electrical Force (N) q – Electrical Charge (C) r – Distance (m)

Practice Problem Calculate the forces that exist between the following pairs of charged particles: –In the hydrogen atom the electron (q = -1.60x C) and the proton (q = +1.60x C) are separated by a distance of 5.29x m. –Two identically charged (q = 1.4x10 -8 C) particles are positioned 1.3x10 -3 m apart. –A particle (q = -3.2x10 -4 C) is positioned m away from a second particle (q = 6.4x C). –Two positively charged particles are positioned 1.1x10 -3 m apart. Particle 1 has a charge of 9.4x10 -5 C while particle 2 has a charge of 3.5x10 -4 C.

Forces Between Multiple Particles When more than 2 particles are interacting each force pair has to be calculated and then all force acting on each object has to be added through vector addition Steps for solving –Identify each pair of forces interacting –Calculate the force acting between each pair of particles –Add all the forces acting on each particle through VECTOR ADDITION Find “X” and “Y” components for each vector Add all “X”s to find X R Add all “Y”s to find Y R Use Pythagorean theorem to find the magnitude of the resultant “Net” force Use TAN -1 of X R and Y R to find the direction of the “Net” force

Practice Problem A B C.0001m m C-0.002C C A C B Tan -1

Problem s 1.If two point charges (q 1 = 8.3x10 -8 C, q 2 = -1.9x10 -8 C) are located 1.05m apart, and a third charge (q 3 =-2.3x10 -8 C) is placed midway between them; what is the net force acting on the third charge? 2.If two point charges (q 1 = 4.3x10 -8 C, q 2 = -1.9x10 -8 C) are located 0.65m apart, and a third charge (q 3 =1.3x10 -8 C) is placed midway between them, what is the net force acting on the third charge? 3.If two point charges (q 1 = 8.3x10 -8 C, q 2 = 1.9x10 -8 C) are located 1.0m apart, and a third charge (q 3 =-2.3x10 -8 C) is placed midway between them and 0.2m above the midline; what is the net force acting on the third charge? 4.Charge 2 (q 2 =1.5x10 -4 C) is located 0.13m to the left of charge 1 (q 1 =-1.01x10 -6 C) while charge 3 (q 3 =5.5x10 -5 C) is located 0.05m directly above charge 1. What is the magnitude and direction of the force acting on charge 3? 5.Charges A (q = 1.3x10 -5 C), B (q = -3.4x10 -4 C) and C (q = 9.3x10 -4 C) form an equilateral triangle with sides 0.015m long. Charge A is on top, with charge B on the lower left. What is the size and direction of the net force acting on Charge A?

Problems 1 & 2 Solutions 1. F 13 = -6.23x10 -5 F 23 = 1.43x10 -5 Draw the vectors! Vectors go in same direction so add! 6.23x x10 -5 = 7.66x10 -5 N Left 2. F 13 = 4.76x10 -5 F 23 = -2.1x10 -5 Draw the vectors! Vectors go in same direction so add! 4.76x x10 -5 = 6.86x10 -5 N Right F 23 F 13 F 23 F 13

Problem 3 Solution q1q1 q3q3 q2q

Electrical Potential Energy Work can be done by electric fields. –When a charged particle enters an electric field the field force acts on the particle –As the particle moves over a certain distance, work is done The position of a charged particle in an electric field relates to electrical potential energy. –The closer a charged particle is to a like charge, the greater the force acting to move the particle, and the greater the potential to do work. –Electrical potential energy is related to the magnitude of the charges producing the field and the distance between the charges. Formula –Electrical Potential Energy for a pair of charges EPE = k c (q 1 q 2 /r) k c = 8.99x10 9 Nm 2 /C 2 q in Coulombsr in meters

Electrical Potential Difference Electrical Voltage The difference in electrical potential energy between two points in an electric field: –Corresponds to difference in height when dealing with gravitational potential energy –Measure of an electric field’s ability to do work. Higher potential energy can do more work The measure of electrical potential energy is voltage (V) –Potential difference (voltage) is the characteristic of electric fields that allows electricity to do work! Without a difference in charge, there is no electric field Without an electric field, there is no force to make electrons move If electrons don’t move they cant do work

Voltage and Electron Flow Voltage relates to differences in electron concentration –A positive region has a need for electrons –A negative region has an excess buildup of electrons –Electrons are negatively charged and repel other electrons Electrons flow from areas of higher (-) to lower (+) concentrations –Connect positively charged (lack of electrons) and a negatively charged (excess of electrons) regions by a material that electrons can flow through and electrons move from negative to positive until the difference in charge is gone –When electrons move they can do work, this is electricity

Batteries and Cells Batteries are devices that use chemical reactions to produce voltage –The positive terminal is connected to a chemical reaction that absorbs electrons –The negative terminal is connected to a chemical reaction that produces electrons –When the two terminals are connected, electrons flow from the negative reaction to the positive reaction A cell is a single set of positive and negative reactions –Large batteries are made up of more than one cell –The voltage produced by a cell depends on the chemical reactions used –Some reactions are reversible, thus batteries with these reactions can be recharged by forcing electrons to flow from positive to negative