18.8 THE ELECTRIC FIELD INSIDE A CONDUCTOR: SHIELDING In conducting materials electric charges move in response to the forces that electric fields exert. Ex. Suppose a piece of copper carriers a number of excess –e somewhere within it. Each –e would experience a force of repulsion because of the electric field of its neighbors. Since copper is a conductor the –e will move due to that force.

They rush to the surface of the copper, because coulomb’s law is affected by distance 1/r^2. Once static equilibrium is established with all of the excess charge on the surface, no further movement of charge occurs. Excess positive charge also moves to the surface of a conductor. At equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor.

The interior of the copper is electrically neutral. No net electric field because no net movement of free electrons. A equilibrium under electrostatic conditions, the electric field is zero at any point within a conducting material.

Fig Uncharged, solid, cylindrical conductor at equilibrium in the central region of a parallel plate capacitor. Induced charges on the surface of the cylinder alter the electric field lines of the capacitor. An electric field cannot exist under these conditions, the electric field lines do not penetrate the cylinder. They end or begin on the induced charges. Test charge placed inside the conductor would feel no force due to the presence of the charges on the capacitor.

The conductor shields any charge within it from electric fields created outside the conductor. The shielding results from the induced charges on the conductor surface. Since the electric field is zero inside the conductor, nothing is disturbed if a cavity is cut from the interior of the material. Stray electric fields are produced by hair dryers, blenders, vacuum cleaners. These stray fields can interfere with the operation of sensitive electronic circuits; stereo amplifiers, tvs, and computers. To eliminate such interference, circuits are often enclosed within metal boxes that provide shielding from external fields.

Fig The electric field just outside the surface of a conductor is perpendicular to the surface at equilibrium under electrostatic conditions.

18.9 GAUSS’ LAW Charge distribution: charges that are spread out over a region, rather than by a single point charge. Gauss’ law describes the relationship between a charge distribution and the electric field it produces. Carl Friedrich Gauss, German mathematician.

Electric flux: – Using both the idea of electric field and surface through which field passes.

GAUSS’ LAW ON A POINT CHARGE Assume point charge is positive. Field line radiate outward in all directions. E = kq/r^2, k can be expressed as k = 1/(4πε o ), where ε o is the permittivity of free space. The equation is: We place this point charge at the center of the imaginary spherical surface of radius r, called the Gaussian surface. A = 4πr^2 so the equation can be written as

EA = magnitude of E of the electric field at any point on the Gaussian surface and the area A of the surface. Electric flux = EA = ϕ E permittivity is the measure of how much resistance is encountered when forming an electric field in a medium, permittivity relates to a material's ability to transmit (or "permit") an electric field. Problems take place in a vacuum, this is where this constant value comes from.

Form of Gauss’ law that applies to a point charge. Electric flux depends only on the charge q within the Gaussian surface and is independent of the radius r of the surface.

Using eq to use with arbitrary shapes. Fig Q = net charge Any arbitrary shape (doesn’t need to be spherical) Must be closed Divided the surface into many tiny sections with area ΔA 1, ΔA 2 and so on. Each section is so small that it is essentially flat and the electric field is a constant.

Electric field magnitude is EcosΦ Φ is the angle between the electric field and the normal. Electric flux through any one section is then (EcosΦ)ΔA The Electric flux that passes through the entire Gaussian surface is the sum of all of these individual fluxes

GAUSS’ LAW

EXAMPLE 15: THE ELECTRIC FIELD OF A CHARGED THIN SPHERICAL SHELL

EXAMPLE 16: THE ELECTRIC FIELD INSIDE A PARALLEL PLATE CAPACITOR

Practice Questions

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