Q.

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).

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answer is 400.

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Detailed Solution

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=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).