91影视

The wis the width of ribbons.

The h is the separation between two ribbons.

The I is the length of the ribbon.

Write the formula ofcapacitance per unit length.

$\mathbf{C}\mathbf{=}\frac{\mathbf{Q}}{\mathbf{V}}$ 鈥︹�� (1)

Here, C is the capacitance and V is the voltage.

Write the formula ofinductance per unit length.

$\mathit{蠒}\mathbf{=}\mathbf{LI}$ 鈥︹�� (2)

Here, L is inductance per unit length and I is the length of the ribbon.

Write the formula ofpropagation speed.

$\mathbf{v}\mathbf{=}\frac{\mathbf{1}}{\sqrt{{\mathbf{渭}}_{\mathbf{0}}{\mathbf{蔚}}_{\mathbf{0}}}}$ 鈥︹�� (3)

Here,${\mathit{蔚}}_{\mathbf{0}}$ is permittivity and${\mathit{渭}}_{\mathbf{0}}$ is permeability.

Write the formula ofpropagation speed.

$\mathbf{L}\mathbf{=}\frac{\mathbf{渭丑}}{\mathbf{w}}$ 鈥︹�� (4)

Here,$\mathit{渭}$ is permeability, h is the separation between two ribbons and w is the width of ribbons.

Now we discuss for a parallel plate capacitor.

The electric field between the plates of the capacitor is

$E=\frac{蟽}{{蔚}_0}$

The potential difference between the plates of capacitor is

$V=Eh$

Then $V=\left(\frac{蟽}{{蔚}_0}\right)h$

But role="math" localid="1657533956022" $蟽=\mathrm{Charge}\mathrm{density}=\frac{Q}{wI}$

Then $V=\frac{1}{{蔚}_0}\left(\frac{Q}{wI}\right)h$

Determine the capacitance per unit length.

Substitute$\frac{1}{{蔚}_0}\left(\frac{Q}{wI}\right)h$ for v into equation (1).

$$\begin{gathered} C=\frac{Q}{{\displaystyle \frac{1}{{蔚}_0}}\left({\displaystyle \frac{Q}{wI}}\right)h} \\ =\frac{{蔚}_{0}wI}{h} \end{gathered}$$

Therefore, the value of capacitance per unit length is$\mathrm{C}=\frac{{\mathrm{蔚}}_0\mathrm{w}\mathrm{I}}{\mathrm{h}}$ .

We know that magnetic field.

$$\begin{gathered} B={渭}_{0}k \\ k=\frac{I}{w} \end{gathered}$$

Then $$\begin{gathered} B=\frac{{渭}_{0}I}{w} \\ 蠒=BhI \end{gathered}$$

Then $=\frac{{渭}_{0}I}{w}hL$

Determine inductance per unit length.

Substitute$\frac{{渭}_{0}IhI}{w}$ for$蠒$ into equation (2).

$$\begin{gathered} \frac{{渭}_{0}IhI}{w}=LI \\ L=\frac{{渭}_{0}IhI}{w} \end{gathered}$$

Then inductance per unit length.

$$\begin{gathered} \frac{L}{I}=L \\ =\frac{{渭}_{0}h}{w} \end{gathered}$$

Therefore, the value of inductance per unit length is $L=\frac{{渭}_{0}h}{w}$.

Derive the propagation speed as follows:

$$\begin{gathered} LC=\frac{{蔚}_{0}w}{h}脳\frac{{渭}_{0}h}{w} \\ ={渭}_0{蔚}_0 \\ =\left(4\mathrm{蟺}脳{10}^{-7}\mathrm{H}/\mathrm{m}\right)\left(8.85脳{10}^{-12}{\mathrm{C}}^2/{\mathrm{Nm}}^2\right) \\ =1.112脳{10}^{-17}{\mathrm{s}}^2/{\mathrm{m}}^2 \end{gathered}$$

Determine the propagation speed.

Substitute $\mathrm{LC}$for$\sqrt{{渭}_0{蔚}_0}$ into equation (3).

$$\begin{gathered} v=\frac{1}{\sqrt{\mathrm{LC}}} \\ =2.999脳{10}^8\mathrm{m}/\mathrm{s} \end{gathered}$$

Therefore, the value of propagation speed $v=2.99脳{10}^8\mathrm{m}/\mathrm{s}$.

As a non-conducting substance with permittivity $蔚$and permeability $渭$separates the strips from one another as follows:

$$\begin{gathered} D=蟽 \\ E=\frac{D}{蔚} \\ E=\frac{蟽}{蔚} \end{gathered}$$

Then solve as:

$$\begin{gathered} C=\frac{蔚w}{h} \\ H=K \\ B=渭H \\ B=渭K \end{gathered}$$

Determine propagation speed.

Substitute$蔚$for$\frac{h}{w}$into equation (4).

localid="1657535319966" $$\begin{gathered} LC=蔚渭 \\ v=\frac{1}{\sqrt{蔚渭}} \end{gathered}$$

Therefore, the value of propagation speed $v=\frac{1}{\sqrt{蔚渭}}$.