102 Capacitance and DielectricsP26.76The electric field due to the charge on the positive wire is perpendicular to the wire, radial, and ofmagnitudeEr+=∈λπ20.The potential difference between wires due to the presence of this charge is∆VddrrDddd10022=−⋅∈=∈−FHGIKJ−+−zzErwirewireln.The presence of the linear charge density −on the negative wire makes an identical contributionto the potential difference between the wires. Therefore, the total potential difference is∆∆VVd==∈−FHGIKJ210bglnand the capacitance of this system of two wires, each of length A, isCQDdd===∈−=∈−λλλπAAA00aflnln.The capacitance per unit length is: CA=∈−0ln.*P26.77The condition that we are testing is that the capacitance increases by less than 10%, or,′<CC110..Substituting the expressions for Cand ′Cfrom Example 26.2, we have,′<CCkkebaebababaAA221.101.10lnlnlnln.ch.This becomes,
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .