Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
History of electromagnetic theory wikipedia , lookup
History of quantum field theory wikipedia , lookup
Superconductivity wikipedia , lookup
Speed of gravity wikipedia , lookup
Lorentz force wikipedia , lookup
Maxwell's equations wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Field (physics) wikipedia , lookup
PHY2054 Announcements Brief recap 1. Discussion section quizzes begin this week! • Chapter 15.1 – 15.4 2. First WebAssign homework due this Friday, 11 pm 3. We will skip Section 15.7 Positive (+) and negative (-) charges Charging by conduction or induction Coulomb’s Law is used to compute electrical forces on charges Questions? Positive charge: E is directed away from the charge Negative charge: E is directed toward the charge Vector law! Electrical fields communicate the presences of other charges Direction of Electric Field Like charges repel and unlike charges attract one another Fundamental charge is e = 1.6 x 10-19 C More fundamental than electrical forces Electric field is a vector quantity Coulomb’s Law F = ke q1 q2 r2 Electric Field E = ke Q r2 (for point charges!) Problem 1 Find the point on the x-axis where the electric field is zero. q1 = +1.0 x 10-6 C q2 = +5.0 x 10-6 C q1 r12 q2 x r12 = 10 cm 1 15.5 Electric Field Lines Positive Point Charge Electric Field Line Patterns Field lines go radially outward A convenient way to visualize electric field patterns Drawing field lines - point in the direction of the field vector at any point Negative Point Charge The field lines are related to the field as follows: Field lines go radially inward The electric field vector E is tangent to the electric field lines at each point The number of lines per unit area through a surface perpendicular to the lines is proportional to strength of the electric field Electric Field Line Patterns An electric dipole consists of two equal and opposite charges The high density of lines between the charges indicates the strong electric field in this region E An electric dipole consists of two equal and opposite charges The high density of lines between the charges indicates the strong electric field in this region Electric Field Line Patterns Example: two equal but like point charges The bulging out of the field lines between the charges indicates the repulsion between the charges The low field lines between the charges indicates a weak field in this region At a great distance from the charges, the field would be approximately that of a single charge of 2q 2 Rules for Drawing Electric Field Lines The lines for a group of charges must begin on positive charges and end on negative charges 15.6 Conductors in Electrostatic Equilibrium For excess of charge, some lines will begin or end infinitely far away The number of lines drawn leaving a positive charge or ending on a negative charge is proportional to the magnitude of the charge No two field lines can cross each other E just outside a charged conductor is perpendicular to the conductor’s surface Consider what would happen it this was not true The component along the surface would cause the charge to move It would not be in equilibrium When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium An isolated conductor has the following properties: The electric field is zero everywhere inside the conducting material Any excess charge on an isolated conductor resides entirely on its surface The electric field just outside a charged conductor is perpendicular to the conductor’s surface On an irregularly shaped conductor, the charge accumulates at locations where the radius of curvature of the surface is smallest (that is, at sharp points) Electric Flux Field lines penetrating an area A perpendicular to the field The product of EA is the electric flux, ΦE In general: ΦE = E A cos θ The perpendicular to the area A is at an angle θ to the field For closed surfaces, the flux lines passing into the interior are negative; those passing out of the interior are positive 3 Simple Example: Electric Field of a Charged Thin Spherical Shell Gauss’ Law Gauss’ Law states that the electric flux through any closed surface is equal to the net charge Q inside the surface divided by εo ΦE = Qinside εo εo is the permittivity of free space and equals 8.85 x 10-12 C2/Nm2 The calculation of the field outside the shell is identical to that of a point charge E= Coulomb constant: ke = 1/4πεo A Gaussian surface does not have to coincide with the surface of a physical object Problem 2 r1 = 10 cm Find: a) The charge on the inner and outer surfaces of the shell b) The distance r2 q1 q2 r2 Use a cylindrical Gaussian surface The flux through the ends is EA r1 The electric field inside the shell is zero Electric Field of a Nonconducting Plane Sheet of Charge q1 = +3.0 x 10-6 C q2 = -1.0 x 10-6 C A solid conducting sphere is located at the center of the spherical conducting shell. The sphere has a total charge q1 and the shell has a total charge q2. The ratio Er1/Er2 = 10 Q Q = ke 2 4πr 2 εo r no field through the curved part of the surface The total charge is Q = σA E= σ is the surface charge density (C/m2) σ 2ε 0 The field is uniform 4 Parallel Plate Capacitor The device consists of plates of positive and negative charge The total electric field between the plates is given by E = σ εo The field outside the plates is zero 5 , ^ '' (f -f %2f?s*tS<Z I .->-,? ?9vh'S* 3 ?K/, a^, ~ 'S.3-! O 7 '"' X .^-^ f" r Cr .^.^;