Page 1 : ——, , le, , put angle between the direc, , al to the surf. tion of, ee Ot the cylinder ds j es, 1S zero., , , , , , , , , By Gauss law,, , 0 7 . ee cos 0 =] TNEI = Total charge, ; e [pe Ecos @ ds|_ + (fe Ecos @ ds}. =, ‘ : ‘ |. = Total charge...(1), 6 ds = Area of curved surface of Gaussian cylinder ae gs density,, ., 0 ee ER =, 6 EX nr Total surface area, 2 --+-(1) Eqn for dielectric medium Ey —, know e= ke, We . a Total charge = o¢ ds., B= Onke,r -+-(2) Since9=0° .. cos0=1, , , , , , , , , , , , , , , , , , , , , For air medium k=1, r, , v+(3), , The direction of electric field E is directed outward if, i. is positive and inward if) is negative., , a 2né,r, , 3., , , , Fig. 8.3 Direction of the field for, two types of charges, , (iii) Electric field due to a charged infinite plane, sheet:, , Consider a uniformly charged infinite plane, sheet with surface charge density 9. By symmetry, electric field is perpendicular to plane sheet and, directed outwards, having same magnitude at a, given distance on either sides of the sheet. Let P be, a point at a distance r from the sheet and E be the, electric intensity at P. cay, To find Electric Intensity due to charged infinite, , sheet at point P,, , (a), , Gaussian, surface, , Equation (1) becomes, , cEfds+cEfds=agds, 2eEgds=cagds, , ie o, . aan, We know for dielectric medium, ¢ = ke,, o, E= Ie, ok, For air medium k= 1, Go, = 26, e-+-(4), , ELECTRIC POTENTIAL AND POTENTIAL ENERGY:, , Let us see first potential energy. We know, that like charges repel and unlike charges attract, each other. A charge exerts a force on any other, charge in its vicinity. Some work is always done to, move a charge in the presence of another charge., Thus potential energy arises from any collection, of charges. We can define P.E. "The electrostatic, potential energy of a system of point charges is, defined as the work required to assemble the system, of charges by bringing them from infinity to their, present locations., , Work done i.e. electric potential energy against, force is dU = F.dr where dU is the electric potential, energy when the charge is displaced through dr and, F -be the force exerted on the charge., , Expression for Potential Energy:, , Consider a charge +Q at point O. Leta small, charge +q, be brought from point A to B at respective, distances r, and r, from O, against force on it., , +Q +o, oc h——} B dr A, , —$— 1, Fig. 8.5 Charge +q, displaced by, dr towards charge +Q, , F, , E, , Work done against the force (F,), in displacing, charge qo through displacement dr is, dU =- F,.dr Sea, , Negative sign indicates displacement (dr) and force, F,, are in opposite direction.