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or, , (i), , , , GAUSS' LAW:, , The total normal electric induction over a closed, , surface is equal to the algebraic sum of the electric, charges enclosed by that surface., TNEI = Sum of all charges, n, gE,E cos 8 ds= 2 q, 1=, , q, gE, E cos 8 ds = —, , 0, , q, Total flux (@) i Sin $ Ecos 6 ds., 0, , APPLICATION OF GAUSS LAW:, , Electric field Intensity due to uniformly charged ., , spherical shell or hollow sphere:, Consider a sphere of radius R with its centre at O,, , charge to a uniform surface charge density o placed., , in a dielectric medium of permittivity «., , q q, We know o = A an, Total charge (q) = o 4nR?, Consider a point P outside the sphere at a distance r, from centre of sphere (O) ie OP = r. Draw a Gaussian, spherical surface with centre O & radius 'r, ds -be the small surface area around Ott, P., , , , on-T=-~, aS, , , , Guassion, Surface, , Fig. 8.1 Uniformly charged, spherical shell or hollow sphere., , By Gauss' law, , PerecesOds=q 1, (1), , The magnitude of electric intensity at every point, on the Gaussian sphere is same and it is directed, radially outward, Also, the angle between the, direction of E and the normal to the surface of the, sphere is zero., , Le.9=0 ". cos@=1, p e Eds = q, eEdids =q, But @ds = Total surface area of Gaussian sphere, = 4n r?, eE4nr?=q, , Pee sl, , , , , , By definition of dielectric constant, , pees ¢=ks0, , , , £, E = 13), Anker, For air medium k= 1, ee A ...(4), a 4né,r, Putting, q = 6 40R?, o 4nR?, B= Aner, oR?, Fie aa}, E Bile, Case I: If point P lies on the surface of the charge |, sphere, r=R, oO, es is, , i r =, Case II: If point P lies inside the sphere: since there are |, , no charges inside o = O, E=0, (ii) Electric field Intensity due to an infinitely long, straight charged wire:, , ON enna tn aatwat sage:, , Consider a uniformly charged wire of infinite, length having a constant linear charge density (i, kept in medium of permittivity e., , Let R -be the radius of cross section of wire., We know, A= =, , ego ge, , , , Total charge (q) =i 1, i t, E, + F, E, ai :, Git feared 4s i., Coo aes E, | as, Potten, Ma : Gaussian, + < Surface, , Fig. 8.2 Infinitely long Straight charged wire., eee , point at a distance 'r from the axis of wire., a te cylindrical Surface of radius r a?, ae # | a in fig 8.2 Let E be electric intensity, es } it is directed radially outward and, , ame for all points at Same distance from the ax!5:, By Gauss law, TNE] = Total charge., $&.E cos 9 ds=}1