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∆VddrrDddDdd10022= −⋅= −∈=∈−FHGIKJ−+−zzErwirewireλπλπln.The presence of the linear charge density −λon the negative wire makes an identical contributionto the potential difference between the wires. Therefore, the total potential difference is∆∆VVDdd==∈−FHGIKJ210bgλπlnand the capacitance of this system of two wires, each of length A, isCQVVDddDdd===∈−=∈−∆∆λλλ ππAAA00bg afaflnln.The capacitance per unit length is: CDddA=∈−π0lnaf.*P26.77The condition that we are testing is that the capacitance increases by less than 10%, or,′<CC1 10..Substituting the expressions for Cand ′Cfrom Example 26.2, we have,′==<CCkkebaebababaAA221 10
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