InterviewSolution
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InterviewSolution
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A silver wire has resistivity `rho=1.62xx10^-8 Omegam` and cross-sectional area `10.0mm^2`. The current in the wire is uniform and changing at the rate of `4000A//s`, when the current is 200A. (a) What is the magnitude of the electric field in the wire when the current in the wire is 200A? (b) What is the displacement current in the wire at that time (c) What is the ration of the magnitude of the magnetic field due to the displacement current to that due to the current at a distance r from the wire? |
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Answer» Here, `rho=1.62xx10^-8Omegam`, `A=10.0xx10^-6m^2=10^-5m^2`. `(dI)/(dt)=4000As^-1, I=200A`. (a) Magnitude of the electric field in the wire when the current in the wire is 200A, is `E=rhoJ=rhol/A=((1.62xx10^-8)xx200)/(10^-5)` `=0.324Vm^-1` (b) The displacement current is `I_D=in_0 (dphi_E)/(dt)=in_0d/(dt)(EA)` `in_0A (dE)/(dt)=in_0Ad/(dt) ((rhol)/A)` `=in_0Axxrho/A((dI)/(dt)) =in_0rho(dl)/(dt)` `=(8.85xx10^-12)x(1.62xx10^-8)xx4000` `=5.74xx10^-6A` (c) Ratio of magnetic fields is `(B("due to" I_d))/(B("due to" I))=(mu_0 I_D//2pir)/(mu_0I//2pir)` `=(I_D)/I=(5.7f4xx10^-16)/200=2.87xx10^-18` |
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