- #1

Boltzman Oscillation

- 233

- 26

- Homework Statement
- A semi-infinite linear conductor extends between z = 0 and z = inf. along the z- axis. If the current in the inductor flows along the positive z-direction find H(vector) at a point in the x-y plane at a distance r from the conductor.

- Relevant Equations
- H = I/(4*pi) Integral[( dl x R)/R^2]

I drew an illustration to make this easier:

Point P is where I wish to find the magnetic flux density H.

Given the Biot-Savart formula:

$$d\textbf{H} = \frac{I}{4\pi}\frac{d\textbf{l}\times\textbf{R}}{R^2}$$

I can let

$$d\textbf{l} = \hat{z}dz$$

and

$$\hat{z}dz\times\textbf{R} = \hat{\phi}sin(\theta_{Rdl})dz$$

Have I done this correctly so far? If so, what should I let R^2 in the Biot-Savart equation be?

Point P is where I wish to find the magnetic flux density H.

Given the Biot-Savart formula:

$$d\textbf{H} = \frac{I}{4\pi}\frac{d\textbf{l}\times\textbf{R}}{R^2}$$

I can let

$$d\textbf{l} = \hat{z}dz$$

and

$$\hat{z}dz\times\textbf{R} = \hat{\phi}sin(\theta_{Rdl})dz$$

Have I done this correctly so far? If so, what should I let R^2 in the Biot-Savart equation be?