Two very similar questions 1) A uniformly charged spherical insulator has a conc

Question

Two very similar questions

1) A uniformly charged spherical insulator has a concentric spherical cavity as illustrated below. If the volume charge density is ?, what is a correct expression for electric field strength E inside the insulating material (fora<r<b)? Use Gauss's Law.

2 )A uniformly charged, infinitely long insulating cylinder is illustrated below. The cylinder has volume charge density ?. What is the electric field strength E inside the insulating material (for r<R)? Use Gauss's Law.

1 Diagram)

Explanation / Answer

1.Using integral of E.dA=Qin/epsilont.......

Consider a sphere at radius r,a<r<b. Integral of E.dA over the sphere of radius r gives E.4pie*r*r..Qin=Volume density*(4/3*pie*r*r*r-4/3*pie*a*a*a).Putting these in 1 we get,

E=p(r^3-a^3)/3r^2epsilon.

2.for r<R,suppose we assume a cylinder of radius r,then Q enclosed by the cylinder i.e. Qin is 0.Accoeding to Gauss law,if Qin =0,then electric field over that loop is 0.Therefore option a.

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