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CONDUCTORS IN ELECTROSTATIC EQUILIBRIUM (19.11) Properties are a result of the following: In a “good” conductor, electrons are free to move. At electrostatic equilibrium, charges MUST feel no force OR ELSE they will move until there is no force One result: charge distribution is generally NON-UNIFORM for: A charged conductor A conductor in an electric field PROPERTIES: ISOLATED CONDUCTOR IN ELECTROSTATIC EQUILIBRIUM st 1 : E 0 everywhere inside a conductor Must be true or else charges would move until E 0 o for conductor in external electric field, charges locate so that superposition of external E plus E from charges gives E 0 inside 2nd: Any NET CHARGE on conductor must be on surface can prove with Gauss’s Law o Choose Gaussian surface JUST INSIDE conductor surface because E 0 inside, normal component of field at Gaussian surface must be zero Because En 0 , must have E En dA 0 qinside q 0 But Gauss’s law says E 0 so inside Because Gaussian surface can be arbitrarily close to the conductor surface, net charge inside conductor must be zero RESULT: ANY NET CHARGE ON THE CONDUCTOR MUST BE ON THE SURFACE 3rd: Electric field JUST OUTSIDE a CHARGED CONDUCTOR: MUST be perpendicular to the surface. If not, charge flows along surface E MUST have magnitude n 0 o is the surface charge density AT THAT point o choose Gaussian cylinder, cross-sectional area A one end inside conductor (where E 0 ) one end outside conductor (where E En ) know E is perpendicular to cond. surface charge inside is qinside A o Only flux through Gaussian surface is through outside cylinder end So: e E dA E n A qinside o Gauss’s law says E 0 E o Result is: n 0 A E A which means n 0 E is perpendicular to surface of charged conductor Neutral conductor in an external E field Field induces charge separation E Field lines bend so that at the surface is always perpendicular 4th: Surface charge density is HIGHEST where radius of surface curvature is smallest Means highest E at most “pointed” regions of surface Will see why later