week3_chapter24_web

week3_chapter24_web - Gauss Law Gauss Law can be used as an...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Week 3: Chapter 24 Gauss’s Law Gauss’ Law Gauss’ Law can be used as an alternative procedure for calculating electric fields. Gauss’ Law is based on the inverse-square behavior of the electric force between point charges. It is convenient for calculating the electric field of highly symmetric charge distributions. Gauss’ Law is important in understanding and verifying the properties of conductors in electrostatic equilibrium. Introduction Electric Flux Electric flux is the product of the magnitude of the electric field and the surface area, A , perpendicular to the field. Φ E = EA Units: N · m 2 / C Section 24.1 Electric Flux, General Area The electric flux is proportional to the number of electric field lines penetrating some surface. The field lines may make some angle θ with the perpendicular to the surface. Then Φ E = EA cos Section 24.1 Electric Flux, Interpreting the Equation The flux is a maximum when the surface is perpendicular to the field. θ = 0 ° The flux is zero when the surface is parallel to the field. θ = 90 ° If the field varies over the surface, Φ = EA cos is valid for only a small element of the area. Section 24.1 Electric Flux, General In the more general case, look at a small area element. In general, this becomes The surface integral means the integral must be evaluated over the surface in question. In general, the value of the flux will depend both on the field pattern and on the surface. cos Ei i ii i EA θ     0 surface lim i i A E d     Section 24.1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Electric Flux, Closed Surface Assume a closed surface The vectors point in different directions. At each point, they are perpendicular to the surface. By convention, they point outward. i A Section 24.1 Flux Through Closed Surface, cont. At (1), the field lines are crossing the surface from the inside to the outside; θ < 90 o , Φ is positive. At (2), the field lines graze surface; = 90 o , Φ = 0 At (3), the field lines are crossing the surface from the outside to the inside;180 o > > 90 o , Φ is negative. Section 24.1 Flux Through Closed Surface, final The net flux through the surface is proportional to the net number of lines leaving the surface. This net number of lines is the number of lines leaving the surface minus the number entering the surface. If E n is the component of the field perpendicular to the surface, then The integral is over a closed surface. En dE d A     EA  ±± Section 24.1 Flux Through a Cube, Example The field lines pass through two surfaces perpendicularly and are parallel to the other four surfaces. For face 1, E = -E l 2 For face 2, E = E 2 For the other sides, E = 0 Therefore, E total = 0 Section 24.1 Karl Friedrich Gauss 1777 – 1855 Made contributions in Electromagnetism Number theory Statistics Non-Euclidean geometry Cometary orbital mechanics A founder of the German Magnetic Union Studies the Earth’s magnetic field Section 24.2 Gauss’s Law, Introduction
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/04/2011 for the course PHYSICS 121 taught by Professor Fayngold during the Spring '10 term at NJIT.

Page1 / 7

week3_chapter24_web - Gauss Law Gauss Law can be used as an...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online