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

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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 = ?

Magnetic energy in terms of I = Wmag = 0.207I² μJ

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

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