边界条件及例题讲解（双语）.pptxVIP

Electrostatic shieldingIf there are no free charges inside of a closed cavity made of conductor, no electrostatic field exists inside the cavity, although charges may exist outside.A closed cavity made of conductor shields its interior from the influence of any electrostatic field outside of it, and this effect is called electrostatic shielding.q = 0E = 0????????If a fictitious closed surface is constructed within the wall of the cavity, the electric flux over the surface must be zero.There is either no charge enclosed by this surface, or it contains positive and negative charges of equal amount. If the former is true, no electric fields can exist inside the cavity. If it is the latter case, there could be electric field inside the cavity. However, it is impossible.The positive and the negative charges only exist on the surface, and the redpath could be an electric field line.??????Then the circulation of the electric field around the entire closed curve will not be zero. That is contrary to the basic property of electrostatic field.??If the cavity is grounded, the charges inside it cannot produce any electrostatic fields outside of it.Example. A conducting sphere of radius r1 and with positive charge q is enclosed by a conducting spherical shell of internal radius r2. The permittivity of the dielectric between the sphere and the shell is ?1, and the external radius of the shell is r3 . The spherical shell is covered by a dielectric of ?2 with external radius r4. The outer region is vacuum.Find: (a) The electric field intensities in every region. (b) The freecharges and the bound charges on each surface.Solution: In view of the spherical symmetry of the structure and the fields, Gauss’ law can been applied.? 2? 1 r2? 0r3 r4r1Taking the spherical surfaces as Gaussian surfaces, it can be seen that the electric field intensities are perpendicular to them.In the regions r r1 and r2r r3 ,E = 0, since electrostatic field cannot exist in conductor