A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length +α, where a is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length +α.
(a) Calculate the electric field in terms of +α and the distance r from the axis of the tube for
(i) r < a; (ii) a < r < b; (iii) r > b. Show your results in a graph of E as a function of r.
(b) What is the charge per unit length on (i) the inner surface of the tube and (ii) the outer surface of the tube?

A) i) E =α/ [2πrL(εo)]

ii) E=0

iii) E = α/(πrεo)

The graph between E and r for the 3 cases is attached to this answer ;

B) i) charge on the inner surface per unit length = - α

ii) charge per unit length on the outer surface = 2α

Explanation:

A) i) For r < a, the charge is in the cavity and takes a shape of the cylinder. Thus, applying gauss law;

EA = Q(cavity) / εo

Now, Qcavity = αL

So, E(2πrL) = αL/εo

Making E the subject of the formula, we have;

E =α/ [2πrL(εo)]

ii) For a < r < b; since the distance will be in the bulk of the conductor, therefore, inside the conductor, the electric field will be zero.

So, E=0

iii) For r > b; the total enclosed charge in the system is the difference between the net charge and the charge in the inner surface of the cylinder.

Thus, Qencl = Qnet - Qinner

Qinner will be the negative of Qnet because it should be in the opposite charge of the cavity in order for the electric field to be zero. Thus;

Qencl = αL - (-αL) = 2αL

Thus, applying gauss law;

EA = Qencl / εo

Thus, E = Qencl / Aεo

E = 2αL/Aεo

Since A = 2πrL,

E = 2αL/2πrLεo = α/(πrεo)

B) i) The charge on the cavity wall must be the opposite of the point charge. Therefore, the charge per unit length in the inner surface of the tube will be - α

ii)Net charge per length for tube is +α and there is a charge of - α on the inner surface. Thus charge per unit length on the outer surface will be = +α - (- α) = 2α

2b2t

explanation:

2b2t

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia