Presentation on theme: "Electric Forces Mr. Burns"— Presentation transcript:
1Electric Forces Mr. Burns SPH4UElectric ForcesMr. Burns
2Maxwell’s EquationsGauss’s Law: The electric field’s mapping is equal to the charge density divided by the permittivity of free space. The relationship between electric field and electric chargeGauss’s Law for Magnetism: The net magnetic flux out of any closed surface is zero. There is no such thing as a magnetic monopoleWe can make an electric field by changing a magnetic fieldThe divergence (del opeerator) measures the magnitude of a vector field’s sourceDel E = dEx/dt+dEy/dt+dEz/dtThe curl operator is the cross product of partial deritatives.We can make a magnetic field with a changing electric field or with a current
3Maxwell’s 1st Equation.Maxwell’s first equation is Gauss’s Law. This equation tells us that electric field lines (E) DIVERGE outward from positive charges and CONVERGE inward to the negative charges.
4Maxwell’s 2nd Equation.Maxwell’s second equation tells us that the magnetic field (B) never DIVERGES or CONVERGE. They always go around in closed loops, therefore there doesn’t exist a single magnetic pole.
5Maxwell’s 3rd Equation.Maxwell’s third equation is Faraday’s Law. This equation tells us that electric field lines (E) CURL around changing magnetic fields (B) and that changing magnetic fields induce electric fields.
6Maxwell’s 4th Equation.Maxwell’s fourth equation tells us that the magnetic field (B) lines CURL around electric currents AND that magnetic field (B) lines CURL around changing electric fields.
7The Origin of Electricity The electrical nature of matter is inherentin atomic structure.coulombs
8The Origin of Electricity In nature, atoms are normallyfound with equal numbers of protonsand electrons, so they are electricallyneutral.By adding or removing electronsfrom matter it will acquire a netelectric charge with magnitude equalto e times the number of electronsadded or removed, N.
9The Origin of Electricity Example 1 A Lot of ElectronsHow many electrons are there in one coulomb of negative charge?
10Charged Objects and the Electric Force It is possible to transfer electric charge from one object to another.The body that loses electrons has an excess of positive charge, whilethe body that gains electrons has an excess of negative charge.
11Charged Objects and the Electric Force LAW OF CONSERVATION OF ELECTRIC CHARGEDuring any process, the net electric charge of an isolated system remainsconstant (is conserved).
12Charged Objects and the Electric Force Like charges repel and unlikecharges attract each other.
14Conductors and Insulators Not only can electric charge exist on an object, but it can also movethrough an object.Substances that readily conduct electric charge are called electricalconductors.Materials that conduct electric charge poorly are called electricalinsulators.
16Charging by Contact and by Induction Charging by induction.
17Charging by Contact and by Induction The negatively charged rod induces a slight positive surface chargeon the plastic.
18Coulomb’s LawThey preferred to think of an object producing a “field” and other objects interacting with that fieldPhysicists did not like the concept of “action at a distance” i.e. a force that was “caused” by an object a long distance awaythey liked to think...Thus rather than ...+--+
20The magnitude of the electrostatic force exerted by one point charge Coulomb’s LawCOULOMB’S LAWThe magnitude of the electrostatic force exerted by one point chargeon another point charge is directly proportional to the magnitude of thecharges and inversely proportional to the square of the distance betweenthem.
21Example 3 A Model of the Hydrogen Atom Coulomb’s LawExample 3 A Model of the Hydrogen AtomIn the Bohr model of the hydrogen atom, the electron is in orbit about thenuclear proton at a radius of 5.29x10-11m. Determine the speed of theelectron, assuming the orbit to be circular.
23Electrostatics Gravitational Force Coulomb’s LawElectrostaticsGravitational ForceTwo types of charges (q): positive and negativeOne type of mass (m): positive massAttraction (unlike charges) and repulsion (like charges)Attraction (all masses)F:Potential energy:
24Gravitational vs. Electrical Force Coulomb’s LawGravitational vs. Electrical ForcerFq1m1q2m2* smallest charge seen in nature!For an electron:* q = 1.6 ´ Cm = 9.1 ´ kgFelecgrav=+4171042.
25That’s smaller than one cell in your body! Coulomb’s LawSuppose your friend can push their arms apart with a force of 450 N. How much charge can they hold outstretched?+Q-Q2mF= 450 N= 4.47•10-4 CThat’s smaller than one cell in your body!
26Example 4 Three Charges on a Line Coulomb’s LawExample 4 Three Charges on a LineDetermine the magnitude and direction of the net force on q1.
31The positive charge experiences a force which is the vector sum of the The Electric FieldThe positive charge experiences a force which is the vector sum of theforces exerted by the charges on the rod and the two spheres.This test charge should have a small magnitude so it doesn’t affectthe other charge.
32(a) (b) Example 6 A Test Charge The Electric FieldExample 6 A Test ChargeThe positive test charge has a magnitude of3.0x10-8C and experiences a force of 6.0x10-8N.Find the force per coulomb that the test chargeexperiences.Predict the force that a charge of +12x10-8Cwould experience if it replaced the test charge.(a)(b)
33DEFINITION OF ELECTRIC FIELD The Electric FieldDEFINITION OF ELECTRIC FIELDThe electric field that exists at a point is the electrostatic force experiencedby a small test charge placed at that point divided by the charge itself:The strength of the electric field can be thought of as the ratio of the force on that charge and the test charge itselfSI Units of Electric Field: newton per coulomb (N/C)
34The Electric FieldIt is the surrounding charges that create the electric field at a given point.
35Electric fields from different sources add as vectors. The Electric FieldElectric fields from different sourcesadd as vectors.
36Example 10 The Electric Field of a Point Charge The isolated point charge of q=+15μC isin a vacuum. The test charge is 0.20mto the right and has a charge qo=+0.8μC.Determine the electric field at point P.
38The electric field does not depend on the test charge. Point charge q:
39Example 11 The Electric Fields from Separate Charges May Cancel Two positive point charges, q1=+16μC and q2=+4.0μC are separated in avacuum by a distance of 3.0m. Find the spot on the line between the chargeswhere the net electric field is zero.
41Conceptual Example 12 Symmetry and the Electric Field Point charges are fixes to the corners of a rectangle in twodifferent ways. The charges have the same magnitudesbut different signs.Consider the net electric field at the center of the rectanglein each case. Which field is stronger?
42THE PARALLEL PLATE CAPACITOR The Electric FieldTHE PARALLEL PLATE CAPACITORcharge densityChange in potential (voltage)Parallel platecapacitorDistance between plates
43in the space surrounding electric charges. Electric Field LinesElectric field lines or lines of force provide a map of the electric fieldin the space surrounding electric charges.
44toward negative charges. Electric Field LinesElectric field lines are always directed away from positive charges andtoward negative charges.
45Electric field lines always begin on a positive charge and end on a negative charge and do not stop inmidspace.
46The number of lines leaving a positive charge or entering a Electric Field LinesThe number of lines leaving a positive charge or entering anegative charge is proportional to the magnitude of the charge.
48Conceptual Example 13 Drawing Electric Field Lines There are three things wrong with part (a) ofthe drawing. What are they?
49The Electric Field Inside a Conductor: Shielding At equilibrium under electrostatic conditions, anyexcess charge resides on the surface of a conductor.At equilibrium under electrostatic conditions, theelectric field is zero at any point within a conductingmaterial.The conductor shields any charge within it fromelectric fields created outside the conductor.
50The Electric Field Inside a Conductor: Shielding The electric field just outside the surface of a conductor is perpendicular tothe surface at equilibrium under electrostatic conditions.