Questions from Electronics

Q: Find the field inside a sphere of linear dielectric material in an

Find the field inside a sphere of linear dielectric material in an otherwise uniform electric field E0 (Ex. 4.7) by the following method of successive approximations: First pretend the field inside is ju...

Q: Is the cross product associative? (A × B)

Is the cross product associative? (A × B) × C =? A × (B × C). If so, prove it; if not, provide a counterexample (the simpler the better).

Q: Construct a vector function that has zero divergence and zero curl everywhere

Construct a vector function that has zero divergence and zero curl everywhere. (A constant will do the job, of course, but make it something a little more interesting than that!)

Q: An uncharged conducting sphere of radius a is coated with a thick

An uncharged conducting sphere of radius a is coated with a thick insulating shell (dielectric constant εr) out to radius b. This object is now placed in an otherwise uniform electric field E0. Find th...

Q: Suppose the region above the xy plane in Ex. 4.

Suppose the region above the xy plane in Ex. 4.8 is also filled with linear dielectric but of a different susceptibility / . Find the potential everywhere.

Q: A spherical conductor, of radius a, carries a charge Q

A spherical conductor, of radius a, carries a charge Q (Fig. 4.29). It is surrounded by linear dielectric material of susceptibility χe, out to radius b. Find the energy of this conï&n...

Q: Calculate W, using both Eq. 4.55 and Eq

Calculate W, using both Eq. 4.55 and Eq. 4.58, for a sphere of radius R with frozen-in uniform polarization P (Ex. 4.2). Comment on the discrepancy. Which (if either) is the “true” energy of the syste...

Q: Two long coaxial cylindrical metal tubes (inner radius a, outer

Two long coaxial cylindrical metal tubes (inner radius a, outer radius b) stand vertically in a tank of dielectric oil (susceptibility χe, mass density ρ). The inner one is maint...

Q: (a) For the configuration in Prob. 4.5

(a) For the configuration in Prob. 4.5, calculate the force on p2 due to p1, and the force on p1 due to p2. Are the answers consistent with Newton’s third law? (b) Find the total torque on p2 with resp...

Q: According to Eq. 4.1, the induced dipole moment

According to Eq. 4.1, the induced dipole moment of an atom is proportional to the external field. This is a “rule of thumb,” not a fundamental law, and it is easy to concoct exceptions—in theory. Suppo...