Question
A long charged cylinder of linear charged density is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?
Solution
Two co-axial cylindrical shells A and B of radii 'a' and 'b' are possessed by a cylindrical capacitor. Assume, 'l' be the length of the cylindrical shell.
Due to the introduction of +q charge on the inner cylindrical shell A, equal but opposite charge –q is induced on the inner surface of the outer cylindrical shell B. The induced charge +q on its outer surface will flow to earth if the shell B is earthed.
The capacitance of the cylindrical capacitor is given as follows, if V is potential difference between the cylindrical shells A and B.
By applying the Gaussian theorem, we first need to find electric field E in the space between two shells to find out potential difference between the cylindrical shells A and B.
Let a cylinder of radius 'r' (such that b > r > a) and length 'l' be the Gaussian surface. Charge enclosed by the Gaussian surface is λl.
where, λ is the charge per unit length on the shell A.
The electric flux will cross through only curved surface of the cylinder (Gaussian surface).
As the area of curved surface of cylinder is 2rl, we have by Gaussian theorem
The field lines are radial and normal to the axis of charged cylinder.
Due to the introduction of +q charge on the inner cylindrical shell A, equal but opposite charge –q is induced on the inner surface of the outer cylindrical shell B. The induced charge +q on its outer surface will flow to earth if the shell B is earthed.
The capacitance of the cylindrical capacitor is given as follows, if V is potential difference between the cylindrical shells A and B.
By applying the Gaussian theorem, we first need to find electric field E in the space between two shells to find out potential difference between the cylindrical shells A and B.
Let a cylinder of radius 'r' (such that b > r > a) and length 'l' be the Gaussian surface. Charge enclosed by the Gaussian surface is λl.
where, λ is the charge per unit length on the shell A.
The electric flux will cross through only curved surface of the cylinder (Gaussian surface).
As the area of curved surface of cylinder is 2rl, we have by Gaussian theorem
The field lines are radial and normal to the axis of charged cylinder.
