Electricity So Far… AP Physics C

Coulomb’s Law and Electric Fields Due to Point Charges (Ch 21) The force between two electric charges which are motionless (static) is given by Coulomb’s law F = kq 1 q 2 /r 2 When more than two charges are present, the force on any one of them can be found using Coulomb’s law and the principle of superposition.

Coulomb’s Law and Electric Fields Due to Point Charges The Electric Field is defined as the force per unit charge E = F/Q Which also gives us F = EQ Electric Field lines –Out from positive –In to negative

Electric Field Lines Review Rules for drawing electric field lines: –Electric field lines begin on positive charges (or at infinity) and end on negative charges (or at infinity) –The lines are drawn symmetrically entering or leaving an isolated charge –The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge –The density of the lines at any point is proportional to the magnitude of the field at that point –At large distances from a system of charges, the field lines are equally spaced and radial, as if they came from a single point charge equal to the net charge of the system –Field lines do not cross

Calculating Electric Fields due to Continuous Charge Distributions The charge distribution is divided into differential regions whose shapes reflect the symmetry of the distribution.

Coulomb’s Law and E Fields from Continuous Charge Distributions

Flux and Gauss' Law Ch 22 AP Physics C

Gauss’s Law Coulomb’s law can be recast into a different form called Gauss’s law which provides a very powerful way to find the electric field when the charge distribution exhibits a high degree of symmetry, such as a sphere, cylinder or plane of charge.

Gauss’s Law Relates the electric field on a closed surface to the net charge within the system For static charges, Gauss’s Law and Coulomb’s Law are EQUIVALENT Gauss’s Law: The net number of lines leaving any surface enclosing the charges is proportional to the net charge enclosed by the surface (Qualitative statement)

Gauss’s Law Gauss’s law is also of greater validity than Coulomb’s law as it applies even when charges move.

How to use Gauss’s Law (Quantitatively) Count the lines leaving a surface as + Count the lines entering a surface as – Figures and on p.738 But this is only quantitative…how do we make calculations? –First we must talk about FLUX (It’s what makes time travel possible)

Flux Flux, in this case Electric Flux, is the amount of (electric) field passing through a specified area. Think of water flowing in a pipe (flux comes from the Latin for “flow”)

Electric Flux Φ The mathematical quantity that corresponds to the number of field lines crossing a surface For a surface perpendicular to the Electric Field, the flux is defined as the product of the magnitude of the field E and the area A: Φ = EA (units are Nm 2 /C)

Electric Flux Φ continued When the area is NOT perpendicular to E, then the following equation is used: Φ = EAcosθ = E n A Where E n is the component of E that is perpendicular or normal to the surface

The box may enclose a charge, by placing a test charge and observing F, we know E. It is only necessary to do this at the surface of the shape.

Pictures of outward (+) flux and inward (-) flux

Situations where the total flux equals zero

The E-field decreases at 1/r 2 while the area increases at r 2 and that increase and decrease cancel each other out and that is why the size of the surface enclosing Q does not matter.

Electric Flux Φ continued What if E varies over a surface? (see Fig on p.739) If we take very small areas A that can be considered a plane, we can then sum the fluxes for each area using Calculus: (does not vary)

Quantitative Statement of Gauss’s Law P740 The net flux through any surface equals 4πk times the net charge inside the surface (Q) OR The net flux through any surface equals the net charge (Q) divided by ε 0

Gauss’ Law

What we can conclude about Ф 1.Ф is proportional to q 2.Whether Ф is inward or outward depends on the q inside the surface 3.A q outside the surface offers zero Ф because Ф in = Ф out

Gauss’ Law The total electric flux through any closed surface is proportional to the net electric charge inside the surface

Calculating Electric Flux P758 #27-36

Finding a Gaussian Surface

Point Charge

Uniformly charge insulator at a varying r

Line of Charge

Sheet of Charge

Calculating Electric Fields and Potentials due to Continuous Charge Distributions The electric potential is easier to calculate because it is a scalar quantity. Once the potential is determined, the electric field can be found by differentiation.

Coulomb’s Law and Electric Fields Due to Point Charges The electric potential (V) is the electric potential energy per unit charge, and the voltage is the difference in potential between two points in space. –Recall the magnitude of any form of potential energy is arbitrary; only differences in potential energy have meaning.