The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
In terms of the dc current I, how much magnetic energy is stored in the insulating medium of a 3-m-long, air-filled section of a coaxial transmission line, given that the radius of the inner conductor is 5 cm and the inner radius of the outer conductor is 10 cm?
Given Information:
Inner radius of conductor = a = 5 cm = 0.05 m
outer radius of conductor = b = 10 cm = 0.10 m
Length of conductor = L = 3 m
Required Reserves = ?
Magnetic energy in terms of I = Wmag = ?
Answer:
Magnetic energy in terms of I = Wmag = 0.207I² μJ
Step-by-step explanation:
The magnetic energy stored in the air-filled coaxial transmission line is given by
Wmag = ½LI²
Where L is the inductance and I is the current
The inductance is given by
L = (μ₀/2π)*ln(b/a)
Where μ₀ is the permeability of free space, a is the inner radius of conductor and b is the outer radius of conductor.
L = (4πx10⁻⁷/2π)*ln(0.10/0.05)
L = 1.386x10⁻⁷ H/m
For a length of 3 meters, the inductance is
L = 3*1.386x10⁻⁷
L = 4.159x10⁻⁷ H
Finally, the magnetic energy in terms of current is
Wmag = ½LI²
Wmag = ½(4.159x10⁻⁷)I²
Wmag = 2.079x10⁻⁷I²
Wmag = 0.207I² μJ