A hollow tube with a rectangular cross-section has external dimensions of 0.5 in by 1 in and a
wall thickness of 0.05 in. Assume that the material is brass, for which the conductivity is
S/m. A DC current of 200 A is flowing through the outer part of the tube.
Calculate the potential difference across an L = 1 m length of the tube in the z direction.
Calculate the potential difference across the same tube that is filled with a second conducting
material with conductivity
Two perfectly-conducting spherical surfaces located the origin have radii rr
= 5.0 cm. A resistive medium with conductivity σ = 0.05 S/m exists between these conductive
surfaces. Given that the total current passing radially outward from surface 1 to surface 2 is
3.0 A, calculate the following quantities:
a. Potential difference V1
between the two conductors,
b. Total resistance R between the two conductors.
c. The electric field intensity
, ,E r inside the resistive medium.
A parallel plate capacitor is filled with a non-uniform dielectric characterized by
2 2 10z z , where z is the height above the bottom plate. If the cross-sectional area is
S = 0.02 m
and d = 1 mm, calculate the total capacitance C.
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