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Announcements. Monday guest lecturer: Dr. Fred Salsbury. Solutions now available online. Will strive to post lecture notes before class. May be different from what you see in class. Start with a single charge and a spherical surface around it. Generalize to any surface.

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announcements
Announcements
  • Monday guest lecturer: Dr. Fred Salsbury.
  • Solutions now available online.
  • Will strive to post lecture notes before class. May be different from what you see in class.
gauss s law

Start with a single charge and a spherical surface around it

Generalize to any surface

Calculate the flux through the sphere

Gauss’s Law
applications of gauss s law
Applications of Gauss’s Law
  • Gauss’s law is always valid.
  • Gauss’s law is not always useful.
  • Most useful in high-symmetry problems where E is uniform in magnitude over all surfaces it penetrates.
  • …and “cute” problems.
application to charge distributions
Application to Charge Distributions

Choosing a Gaussian Surface:

  • The field over the surface is constant through symmetry.
  • The field, E and the surface vector, dA are parallel simplifying the dot product to an algebraic product.
  • … or they are perpendicular, making the dot product zero.
  • The field is zero over the surface.
conceptest
ConcepTest
  • The electric charge per unit area is +σ for plate 1 and –σ for plate 2. The magnitude of the electric field associated with plate 1 iss/eo, and the electric field lines for this plate are as shown. When the two are placed parallelto one another, the magnitude of the electric field is
  • 2σ/εobetween, 0 outside.
  • 2σ/εo between, ±σ/εo outside.
  • zero both between and outside.
  • ±σ/εoboth between and outside.
  • none of the above.
conductors in equilibrium
Conductors in Equilibrium
  • Put a conductor in an electric field.
  • The free electrons inside the conductor will accelerate in the opposite direction of the field lines.
  • As the negative and positive charges separate, an internal field opposing the external field will be established.
  • The acceleration of charges will continue until the internal field cancels out the external field and the conductor will reach electrostatic equilibrium.
  • The electric field is zero everywhere inside a conductor at electrostatic equilibrium.
conductors and gauss s law
Conductors and Gauss’s Law
  • Take a Gaussian surface inside a conductor that is arbitrarily close to the surface.
  • Since the electric field inside the conductor (and hence on the Gaussian surface) is zero, there is no net charge inside the surface.
  • Since the surface is arbitrary, and can be made infinitesimally close to the outer surface of the conductor, any net charge on a conductor will reside on the surface.
conductors and gauss s law1
Conductors and Gauss’s Law
  • The flux through the top surface is EA, since E is perpendicular to A (electrostatic equilibrium).
  • Therefore the flux is zero through the side wall outside the conductor.
  • The field, and hence the flux, through the surfaces inside the conductor are also zero.
conductors and gauss law
Conductors and Gauss’ Law
  • The electric field is zero everywhere inside a conductor at electrostatic equilibrium.
  • Any net charge on a conductor will reside on the surface.
  • The electric field just outside a conductor is perpendicular to the surface and is proportional to the charge density.
  • The charge density is highest near parts of the conductor with the smallest radius of curvature.
a sphere inside a spherical shell
A Sphere Inside a Spherical Shell

r < a

a < r < b

b < r < c

r > c

summary
Summary
  • Flux through any closed surface is proportional to the net charge enclosed by the surface.
  • Use symmetry to simplify calculations.
  • All excess charge on a conductor will reside at the outer surface. The field inside the conductor is zero.