Questions from Electronics

Q: A more elegant proof of the second uniqueness theorem uses Green’s identity

A more elegant proof of the second uniqueness theorem uses Green’s identity (Prob. 1.61c), with T = U = V3. Supply the details.

Q: Find the force on the charge +q in Fig.

Find the force on the charge +q in Fig. 3.14. (The xy plane is a grounded conductor.)

Q: (a) Using the law of cosines, show that Eq

(a) Using the law of cosines, show that Eq. 3.17 can be written as follows: where r and θ are the usual spherical polar coordinates, with the z axis along the line through q. In this form...

Q: In Ex. 3.2 we assumed that the conducting sphere

In Ex. 3.2 we assumed that the conducting sphere was grounded (V= 0). But with the addition of a second image charge, the same basic model will handle the case of a sphere at any potential V0 (relativ...

Q: A hydrogen atom (with the Bohr radius of half an angstrom

A hydrogen atom (with the Bohr radius of half an angstrom) is situated between two metal plates 1 mm apart, which are connected to opposite terminals of a 500 V battery. What fraction of the atomic ra...

Q: A sphere of radius R carries a polarization P(r

A sphere of radius R carries a polarization P(r) = kr, where k is a constant and r is the vector from the center. (a) Calculate the bound charges σb and ρb. (b) Find the field inside and outside the sp...

Q: A short cylinder, of radius a and length L, carries

A short cylinder, of radius a and length L, carries a “frozen-in” uniform polarization P, parallel to its axis. Find the bound charge, and sketch the electric field (i) for L(( a, (ii) for L

Q: Calculate the potential of a uniformly polarized sphere (Ex. 4

Calculate the potential of a uniformly polarized sphere (Ex. 4.2) directly from Eq. 4.9.

Q: A very long cylinder, of radius a, carries a uniform

A very long cylinder, of radius a, carries a uniform polarization P perpendicular to its axis. Find the electric field inside the cylinder. Show that the field outside the cylinder can be expressed in t...

Q: When you polarize a neutral dielectric, the charge moves a bit

When you polarize a neutral dielectric, the charge moves a bit, but the total remains zero. This fact should be reflected in the bound charges σb and ρb. Prove from Eqs. 4.11 and 4.12 that the total bo...