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Chapter 22

# PHYS 241 Chapter 22 Notes.docx

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School
Purdue University
Department
Physics
Course
PHYS 24100
Professor
Oanas Malis
Semester
Fall

Description
Chapter 22 Section 1—Calculating E from Coulomb’s Law • Coulomb’s law states that the electric field dE at a field point P due to this element of charge is: dE=dErhat=(kdq/r^2)*rhat where rhat is a unit vector directed away from the charge element dq and toward point P • Total field E at P is calculated by integrating the expression k̂ E= ∫E= ∫ 2 dq o r Section 2—Gauss’s Law • In electrostatics, Gauss’s Law and Coulomb’s Law are equivalent • The number of electric field lines beginning on the positive charge and penetrating the surface from the inside depends on where the surface is drawn, but any line penetrating the surface from the inside also penetrates it from the outside • To count the net number of lines out of any closed surface, count any penetration from the inside as +1, and any penetration from the outside as -1 • The net number of lines out of any surface enclosing the charges is proportional to the net charge enclosed by the surface • The mathematical quantity that corresponds to the number of field lines penetrating a surface is called the electric flux ∅=EA o o Units are Nm^2/C o Flux is proportional to the number of field lines penetrating the surface • The net flux out of a spherical surface that has a point charge Q at its center is independent of the radius R of the sphere and is equal to Q divided by eo. • The number of lines is the same for all closed surfaces surrounding the charge, independent of the shape of the surface. • o Reflects the fact that the electric field due to a single point charge varies inversely with the square of the distance from the charge o Valid for all surfaes and all charge distributions Section 3—Using Symmetry to Calculate E with Gauss’s Law • Three classes of symmetry to consider: o cylindrical (or line) symmetry if the charge density depends only on the distance from a line o plane symmetry if the charge density depends only on the distance from a place o spherical (or point) symmetry if the charge density depends only on the distance from a point E n Section 4—Discontinuity of • We have seen that the electric field for an infinite plane of charge and a
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