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 outconductor is 10 cm? Use two methods. One is to take the coaxial line an inductor and calculate the energy using. The other is integrate the energy density over the volume.

The answer is 138.5

Explanation:

STEP 1:

The inductance per unit length of a coaxial transmission line is

L′=L / I

=Ø/H

=μoI/2π In (b/a)

In this a is the radius of inner conductor

b is the radius of outer conductor

I is the coaxial transmission

μ is the magnetic permeability

Since the transmission of the charge exists in air, the value of the relative permeability is μr = I and permeability of free space is μo = 4π x 10-7 H/m. So the magnetic permeability will be

μ = μoμ r

μ = μ o (I) 4π x 10-7 H/m

L′ = μoI/2π In (b/a)

= (4π x 10-7) (2) / 2π In (10/5)

=2.77 x 10-7 H

STEP 2:

Obtain the magnetic energy stores in the magnetic field H of a volume of the coaxial transmission line containing a material with permeability μ, by using the formula given below:

Wm = 1/2 LI^2

= 1/2 (2.77x 10^-7 I^2

= 138.5 X 10^-9 I^2 J

Now we will simplify the equation

Wm = 185.5I^2 nJ

So, the magnetic energy stored in insulating medium is 185.5I^2 nJ