In an insulating medium of dielectric constant 1, ρ(y) = by, where b>0. The electric field is zero at y=0 and everywhere is directed along the y-axis. The electric field is:
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Question

In an insulating medium of dielectric constant 1, ρ(y) = by, where b>0. The electric field is zero at y=0 and everywhere is directed along the y-axis. The electric field is:

G1 Physics · Accepted Answer

Since E ⃗ \vec{E} E = E y ( y ) ȷ ^ , E_y(y)ĵ, E y ​ ( y ) ȷ ^ ​ , Gauss's differential law gives d E y / d y E_y/dy E y ​ / d y = ρ/ε₀ = by/ε₀. Using E y ( 0 ) = 0 , E_y(0)=0, E y ​ ( 0 ) = 0 , E y ( y ) E_y(y) E y ​ ( y ) = ∫₀ʸ (by′/ε₀)dy′ = by²/(2ε₀). Thus, E ⃗ \vec{E} E = (by²/2ε₀)ĵ.

In an insulating medium of dielectric constant 1, ρ(y) = by, where b&gt;0. The electric field is zero at y=0 and everywhere is directed along the y-axis. The electric field is:

In an insulating medium of dielectric constant 1, ρ(y) = by, where b>0. The electric field is zero at y=0 and everywhere is directed along the y-axis. The electric field is: