Question

H in the region \( 0 \leq l \leq a \) for an infinitely long co-axial transmission line is:

• A. \( H = \frac{I}{2\pi a^2} \)
• B. \( H = \frac{I}{\pi a^2} \)
• C. \( H = 0 \)
• D. \( H = \frac{I^3}{\pi a^2} \)

Hint:

Ampère’s Circuital Law is used to find the magnetic field in systems with symmetrical current distributions.

Answer 1

The Correct Option is A

Step 1: The magnetic field intensity \( H \) for an infinitely long coaxial transmission line can be determined using Ampère’s Circuital Law: \[ \oint_C \mathbf{H} \cdot d\mathbf{l} = I_{\text{enc}} \] Step 2: Consider a circular Amperian loop of radius \( l \), where the enclosed current for \( 0 \leq l \leq a \) is: \[ I_{\text{enc}} = I \frac{l^2}{a^2} \] Step 3: By applying Ampère’s Law: \[ H \cdot (2\pi l) = I \frac{l^2}{a^2} \] Solving for \( H \): \[ H = \frac{I}{2\pi a^2} \]