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Chapter 22

# PHYS 241 Chapter 22 Notes.docx

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Purdue University

Physics

PHYS 24100

Oanas Malis

Fall

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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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