Consider a long wire in the air (a thin perfectly conducting cylinder of infinite length) of radius r0 and charge per unit length q Cm−1 . (a) State Gauss’ law for the electric flux density D. (b) The electric flux density D outside the wire varies with the radial distance r from the center of the wire. Use Gauss’ law to calculate the electric flux density D as a function of r for r larger than the radius of the wire. (c) What is the equation relating electric field E to electric flux density D in air? What is the electric field E as a function of r for r larger than r0? (d) Suppose we measure voltages relative to a point g outside the wire that is a radial distance rg from the center of the wire. Write down an integral for the voltage V of the wire relative to the point g. (e) The capacitance of the wire per unit length is defined as q/V . If the radius r0 of the wire increases, how does the capacitance per unit length change? Explain.
Consider a long wire in the air (a thin perfectly conducting cylinder of
infinite length) of radius r0 and charge per unit length q Cm−1
.
(a) State Gauss’ law for the electric flux density D.
(b) The electric flux density D outside the wire varies with the radial distance r
from the center of the wire. Use Gauss’ law to calculate the electric flux density D
as a function of r for r larger than the radius of the wire.
(c) What is the equation relating electric field E to electric flux density D in air?
What is the electric field E as a function of r for r larger than r0?
(d) Suppose we measure voltages relative to a point g outside the wire that is a radial
distance rg from the center of the wire. Write down an integral for the voltage V of
the wire relative to the point g.
(e) The capacitance of the wire per unit length is defined as q/V . If the radius r0
of the wire increases, how does the capacitance per unit length change? Explain.
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