Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count...

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Gauss’s Law AP Physics C

Transcript of Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count...

Page 1: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Gauss’s Law

AP Physics C

Page 2: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

How to use Gauss’s Law

Count the lines leaving a surface as +Count the lines entering a surface as –Figures 23-10 and 23-11 on p.696

Page 3: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

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

Page 4: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

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 Nm2/C)

Page 5: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

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.

Page 6: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

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

Page 7: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Electric Flux Φ continued

When the area is NOT perpendicular to E, then the following equation is used:

Φ = EAcosθ = EnA

Where En is the component of E that is perpendicular or normal to the surface

Page 8: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

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”)

Page 9: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.
Page 10: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Situations where the total flux equals zero

Page 11: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Ф = 0 through triangular prism below.

E = 500 N/C

40 cm

50 cm

30 cm40 cm

Page 12: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

The E-field decreases at 1/r2 while the area increases at r2 and that increase and decrease cancel each other out and that is why the size of the surface enclosing Q does not matter.

Page 13: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Electric Flux Φ continued

What if E varies over a surface? (see Fig 23-14 on p.697)

If we take very small areas A that can be considered a plane, we can then sum the fluxes for each area using Calculus

Page 14: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Flux

Symbol ФE

Unit Nm2/CEquation:

AdE

EAAE

E

E

cos

Page 15: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Quantitative Statement of Gauss’s Law

P698The net flux through any surface equals

4πk times the net charge inside the surface

Page 16: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Gauss’ Law

0

4enclosedE enclosed

QE dA kQ

Page 17: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

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 Фin = Фout

Page 18: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Point Charge

Page 19: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Line of Charge

Page 20: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Sheet of Charge

Page 21: Gauss’s Law AP Physics C. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11.

Uniformly charge insulator at a varying r


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