Question

: An infinitly long insulating cylinder of radious R has a volume charge density that varies with the radious as 0 ( ) r a b     , where a and b are positive constants and r is the distance from the axis of the cylinder.use Gausses law to determine the magnitude of the electric field at radial distances a) r < R b) r > R

Answer 1

Imagine a point at (r) inside the cylinder (r <R), the charge assosiated with in this point is, direide = o(r)dV = a[e-*]cameron) - 21 [aros e linice = [27120 ardr - 209[*ura-55] m2 -dr = 271 2 3 Applying Gauss law enclosed sphere of radius r is, DEDA= E E $dA= (Paris) (20) = -(ma[7]) 33 por 27 2 En 36 b → Imagine a point at (r) outside the cylinder (r > R), the charge assosiated with in this point is, doutsile = o(r)dV = A[4-6.](2rtindr) = 204 [art die Louride = 1* 276 ardr - der =271 [barar-lo AR2 R3 = 21,00 2 36 Applying Gauss law enclosed sphere of radius r is, DELA- E $da = (laste) 3(201)=-(2012[1 aR2 3 El 2 36 2R 36 28