In an insulating medium (dielectric$$ constant $$=$$ $$1) the charge density varies with y $$co-ordinate$$ as ρ$$=50$$ε$$0y$$ $$C/m3$$. The electric field is zero at y $$=$$ $$0$$ and everywhere else it is along y direction. Find the electric field at y $$=$$ $$4$$ m (in$$ $$N/C).

Question

In an insulating medium (dielectric$$ constant $$=$$ $$1) the charge density varies with y $$co-ordinate$$ as ρ$$=50$$ε$$0y$$ $$C/m3$$. The electric field is zero at y $$=$$ $$0$$ and everywhere else it is along y direction. Find the electric field at y $$=$$ $$4$$ m (in$$ $$N/C).

Infinity Learn · Accepted Answer

Consider a cylindrical Gaussian surface as shown.

$\begin{array}{l} (E + dE) A - EA = \frac{ρAdy}{ε_{0}} \\ dE = \frac{50 ε_{0} ydy}{ε_{0}} \\ ∴ \int_{0}^{E} dE = \frac{50 ε_{0}}{ε_{0}} \int_{0}^{y} ydy \Rightarrow E = \frac{50 ε_{0} y^{2}}{2 ε_{0}} = \frac{50 ε_{0} \times 16}{2 ε_{0}} = 400 N / C \end{array}$

Gauss's law and its applications

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In an insulating medium (dielectric constant = 1) the charge density varies with y co-ordinate as $ρ = (50 ε_{0}) y C / m^{3}$ . The electric field is zero at y = 0 and everywhere else it is along y direction. Find the electric field at y = 4 m (in N/C).

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Gauss's law and its applications

Remember concepts with our Masterclasses.

In an insulating medium (dielectric constant = 1) the charge density varies with y co-ordinate as ρ=50ε0y C/m3. The electric field is zero at y = 0 and everywhere else it is along y direction. Find the electric field at y = 4 m (in N/C).

Consider a cylindrical Gaussian surface as shown.(E+dE)A−EA=ρAdyε0dE=50ε0ydyε0∴∫0E dE=50ε0ε0∫0y ydy⇒E=50ε0y22ε0=50ε0×162ε0=400N/C

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In an insulating medium (dielectric constant = 1) the charge density varies with y co-ordinate as $ρ = (50 ε_{0}) y C / m^{3}$ . The electric field is zero at y = 0 and everywhere else it is along y direction. Find the electric field at y = 4 m (in N/C).