# Sample Problem GAUSS Law

Sample Problem GAUSS Law

a cross section of a spherical metal shell of inner radius R. A point charge of -5.0 IlC is located at a distance R/2 from the center of the shell If the shell is electrically neutral what are the (induced) charges on its inner and outer surfaces’ Are those charges distribution distributed What is the field pattern inside and outside the shell a cross section of a spherical Gaussian surface within the metal. just outside the inner wall of the shell One Key Idea here is that the electric field must be zero inside the metal and thus on the Gaussian surface inside the metal This means that the electric flux through the Gaussian surface must also be zero Gauss’ law then tells us that the /IN charge enclosed b) the Gaussian surface must be zero With a point charge of
– 5.0 IlC within the shell a charge of must lie on the inner wall of the shell If the point charge were centered. this positive charge would be uniformly distributed along the inner wall However since the point charge is off-center the distribution of positive charge is skewed as suggested by because the positive charge tends to collect on the section of the inner wall nearest the (negative) point charge A second Key Idea that because the shell is electrically neutralist inner wall can have a charge of only if electrons with a total charge of leave the inner wall and move to the outer wall There they spread out uniformly as is also suggested A negative point charge is located within a spherical metal shell that is electrically neutral (11) As a result positive charge i non uniformly distributed on the inner wall of the shell and an equal amount of negative charge is uniformly distributed on the outer     This distribution of negative charge is uniform because the shell is spherical and because the skewed distribution of positive charge on the inner wall cannot produce an electric field in the shell to affect the distribution of charge on the outer law The field lines inside and outside the shell are gown approximately All the field lines intersect the shell and the point charge perpendicularly Inside the shell the pattern of field lines is skewed owing to the skew of the positive charge distribution Outside the shell the pattern is the same as if the point charge were centered and the shell were miss m In fact this would be true no matter where inside the shell the point charge happened robe located ball of charge -SOs lies at the center of hollow spherical metal shell that has a net charge of – l OD What is the charge on (a) the shell’s inner surface and (b) stouter surface.