Question

About the Semi-Quantitative Section This section is halfway between the Qualitative and Quantitative Sections. Use more words, more equations, and more figures than you used in the Qualitative Section. If you have questions, ask me. 12] inside and outside of a charged conducting slab [13] inside and outside of a charged conducting spherical shell [14] inside and outside of an infinitely long charged conducting cylindrical shell [15] inside and outside of a charged conducting box the slab has infinite extent along x and y and finite thickness along z the box has the shape of the surface of the slab

Answer 1

12). Inside the conductor the electric fields due to induced charges are in the same direction but in the opposite direction to the external electric field and add up with a magnitude equal to the magnitude of the electric field. Thus the net electric field in the conductor is zero.

13). The electric field immediately above the surface of a conductor is directed normal to that surface. Now, the gaussian surface encloses no charge, since all of the charge lies on the shell, so it follows from Gauss' law, and symmetry, that the electric field inside the shell is zero. The electric field of a conducting sphere with charge Q can be obtained by a straightforward application of Gauss' law. Considering a Gaussian surface in the form of a sphere at radius r > R , the electric field has the same magnitude at every point of the surface and is directed outward. The electric flux is then just the electric field times the area of the spherical surface. The electric field is seen to be identical to that of a point charge Q at the center of the sphere. Since all the charge will reside on the conducting surface, a Gaussian surface at r< R will enclose no charge, and by its symmetry can be seen to be zero at all points inside the spherical conductor.

14). The electric field of an infinite cylinder of uniform volume charge density can be obtained by a using Gauss' law. Considering a Gaussian surface in the form of a cylinder at radius r > R, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder. The electric field inside an infinite cylinder of uniform charge is radially outward (by symmetry), but a cylindridal Gaussian surface would enclose less than the total charge Q. The charge inside a radius r is given by the ratio of the volumes.

15). Gauss's law can be used to show that the direction of the electric field at the surface of any conductor is always perpendicular to the surface. The magnitude of the electric field just outside a charged conductor is proportional to the surface charge density σ.