Unformatted text preview: J = σ E , Gauss’s law ∇· E = ρ ± o and the continuity equation ∂ρ ∂t + ∇· J = 0 can be used together to derive a di´erential equation ∂ρ ∂t + σ ± o ρ = 0 for the charge density ρ . b) ±ind the solution of the di´erential equation above for t > if at t = 0 the charge density is ρ ( x, y, z, 0) = cos(100 x ) C/m 3 over all space. c) According to the solution found in part (b), how long would it take for ρ to reduce to . 01 cos(100 x ) C/m 3 ? Assume that σ = 5 . 8 × 10 7 S/m. 4. If E = cos( ωtβz ) ˆ x V m , ω β = c , and μ = μ o , ²nd the corresponding H by using ±araday’s law ∇× E =∂ B ∂t . 5. If H = cos( ωt + βz ) ˆ y A m , σ = 0 , ω β = 2 3 c and ± = 2 . 25 ± o , ²nd the corresponding E by using Ampere’s law ∇× H = J + ∂ D ∂t in which J = σ E and D = ± E . 1...
View
Full Document
 Summer '08
 Kim
 Elementary algebra, Electric charge, web site, 1 m, σ, charge density

Click to edit the document details