Question

THE ELECTRIC FIELD AT POINT NEAR AN INFINITE THIN SHEET OF CHARGED CONDUCTOR IS

Answer 1

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The electric field at a point near an infinite thin sheet of charged conductor is:-

18 hours ago

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the electric flux through each cap isΦ1=E.dS=EdS cos 00=EdSAt the points on the curved surface,the field vector E and area vector dS make an angle of900 with each other.So, φ2=E.dS=EdS cos 900=0Therefore,cylindrical surface does not contribute to the flux.Hence, the total flux through the closed surface isΦ=φ1+φ1+ φ2 (there are two end caps)Or φ=EdS+EdS+0=2EdS (1)Now according to Gauss’s law for electrostaticsΦ=q/ε0 (2)Comparing equations (1) and (2),we get2EdS=q/ε0Or E=q/2ε0dS (3)The area of sheet enclosed in the Gaussian cylinder is also dS. Therefore,the charge contained in the cylinder,q=σdS (σ=q/dS)Substituting this value of q in equation (3),we getE=σdS/2ε0dSOr E=σ/2ε0