When an uncharged conducting sphere of radius a is placed at the origin of an x y z coordinate system that lies in an initially uniform electric field 𝐄=E0 𝐤̂, the resulting electric potential is V(x, y, z)=V0 for points inside the sphere and V(x, y, z)=V0-E0 z (E0 a^3 z)/((x^2 y^2 z^2)^3 / 2) for points outside the sphere, where V0 is the (constant) electric potential on the conductor. Use this equation to determine the x, y, and z components of the resulting electric field. | Numerade
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Our formula for the dielectric sphere can actually serve to describe a metal sphere in a uniform field. To demonstrate this, investigate the limiting case, ϵ→∞, and show that the external field then takes on a form which satisfies the perfect-conductor boundary conditions. What about the internal field? Make a sketch of some field lines for this limiting case. How large is the dipole moment induced in a conducting sphere of radius a, in a field E0 ? What is the radius of a conducting sphere with
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