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Problem 15

Let V=10(ρ+1)z2cosϕV in free space. (a) Let the equipotential surface V=20 V define a conductor surface. Find the equation of the conductor surface. (b) Find ρ and E at that point on the conductor surface where ϕ= 0.2π and z=1.5.(c) Find |ρS| at that point.

Problem 16

A coaxial transmission line has inner and outer conductor radii a and b. Between conductors \((a<\rho

Problem 17

Given the potential field V=100xz/(x2+4)V in free space: (a) Find D at the surface z=0.(b) Show that the z=0 surface is an equipotential surface. ( c ) Assume that the z=0 surface is a conductor and find the total charge on that portion of the conductor defined by \(0

Problem 18

Two parallel circular plates of radius a are located at z=0 and z=d. The top plate (z=d) is raised to potential V0; the bottom plate is grounded. Between the plates is a conducting material having radial-dependent conductivity, σ(ρ)=σ0ρ, where σ0 is a constant. (a) Find the ρ -independent electric field strength, E, between plates. (b) Find the current density, J between plates. ( c ) Find the total current, I, in the structure. (d) Find the resistance between plates.

Problem 19

Let V=20x2yz10z2 V in free space. (a) Determine the equations of the equipotential surfaces on which V=0 and 60 V.(b) Assume these are conducting surfaces and find the surface charge density at that point on the V=60 V surface where x=2 and z=1. It is known that 0V60 V is the field-containing region. (c) Give the unit vector at this point that is normal to the conducting surface and directed toward the V=0 surface.

Problem 21

Let the surface y=0 be a perfect conductor in free space. Two uniform infinite line charges of 30nC/m each are located at x=0,y=1, and x=0,y=2(a) Let V=0 at the plane y=0, and find V at P(1,2,0). (b) Find E at P.

Problem 24

At a certain temperature, the electron and hole mobilities in intrinsic germanium are given as 0.43 and 0.21 m2/Vs, respectively. If the electron and hole concentrations are both 2.3×1019 m3, find the conductivity at this temperature.

Problem 25

Electron and hole concentrations increase with temperature. For pure silicon, suitable expressions are ρh=ρe=6200T1.5e7000/TC/m3. The functional dependence of the mobilities on temperature is given by μh=2.3×105T2.7 m2/Vs and μe=2.1×105T2.5 m2/Vs, where the temperature, T, is in degrees Kelvin. Find σ at: (a) 0C;(b)40C;(c)80C.

Problem 27

Atomic hydrogen contains 5.5×1025 atoms /m3 at a certain temperature and pressure. When an electric field of 4kV/m is applied, each dipole formed by the electron and positive nucleus has an effective length of 7.1×1019 m. (a) Find P. (b) Find ϵr.

Problem 29

A coaxial conductor has radii a=0.8 mm and b=3 mm and a polystyrene dielectric for which ϵr=2.56. If P=(2/ρ)aρnC/m2 in the dielectric, find (a) D and E as functions of ρ;(b)Vab and χe(c) If there are 4×1019 molecules per cubic meter in the dielectric, find p(ρ)

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