Q: A conducting sphere at potential V0 is half embedded in linear dielectric
A conducting sphere at potential V0 is half embedded in linear dielectric material of susceptibility χe, which occupies the region z (a) Write down the formula for the proposed potential V...
See AnswerQ: A point charge q is situated a large distance r from a
A point charge q is situated a large distance r from a neutral atom of polarizability α. Find the force of attraction between them.
See AnswerQ: According to Eq. 4.5, the force on a
According to Eq. 4.5, the force on a single dipole is (p. ∇)E, so the net force on a dielectric object is / [Here Eext is the field of everything except the dielectric. You might assume that it wouldn...
See AnswerQ: In a linear dielectric, the polarization is proportional to the field
In a linear dielectric, the polarization is proportional to the ï¬eld: / If the material consists of atoms (or nonpolar molecules), the induced dipole moment of each one is likewise pr...
See AnswerQ: (a) If A and B are two vector functions,
(a) If A and B are two vector functions, what does the expression (A. ∇)B mean? (That is, what are its x , y, and z components, in terms of the Cartesian components of A, B, and ∇?) (b) Compute (rˆ ·...
See AnswerQ: Check the Clausius-Mossotti relation (Eq. 4.72
Check the Clausius-Mossotti relation (Eq. 4.72) for the gases listed in Table 4.1. (Dielectric constants are given in Table 4.2.) (The densities here are so small that Eqs. 4.70 and 4.72 are indisting...
See AnswerQ: The Clausius-Mossotti equation (Prob. 4.41)
The Clausius-Mossotti equation (Prob. 4.41) tells you how to calculate the susceptibility of a nonpolar substance, in terms of the atomic polarizability α. The Langevin equation tells yo...
See AnswerQ: In Fig. 4.6, p1 and p2 are (
In Fig. 4.6, p1 and p2 are (perfect) dipoles a distance r apart. What is the torque on p1 due to p2? What is the torque on p2 due to p1? [In each case, I want the torque on the dipole about its own ce...
See AnswerQ: A (perfect) dipole p is situated a distance z above
A (perfect) dipole p is situated a distance z above an inï¬nite grounded conducting plane (Fig. 4.7). The dipole makes an angle θ with the perpendicular to the plane. Find...
See AnswerQ: Show that the energy of an ideal dipole p in an electric
Show that the energy of an ideal dipole p in an electric ï¬eld E is given by
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