Edits to “Statement”, “Solution”, “Answer”
en/11.3.8.md
+12 −4
| @@ -1,15 +1,22 @@ | |||
| ### Statement | |||
| − | $11.3.8.$ | ||
| + | $11.3.8.$ | ||
| + | Determine the inductance of the unit length of a two-wire line consisting of | ||
| + | two thin flat busbars with a width of d = 0.1 m, located at a distance of h = 5 | ||
| + | mm from each other. The busbars flow modulo equal but oppositely directed | ||
| + | currents. | ||
| + | |||
| ### Solution | |||
| − | For two thin conducting flat plates of width d separated by a distance" h (h \ll d)$, equal and opposite currents produce a practically uniform magnetic field in the space between them. Applying Ampère's law to a rectangular path that crosses one plate, we obtain $H = I/d $and$ B = \mu_0 I/d$ | ||
| + | For two thin conducting flat plates of width d separated by a distance" $h (h \ll d)$, equal and opposite currents produce a practically uniform magnetic field in the space between them. Applying Ampère's law to a rectangular path that crosses one plate, we obtain $ H = I/d $ and $ B = \mu_0 I/d $ | ||
| The magnetic flux per unit length crossing the area$ h \times 1 $between the plates is | |||
| − | $ \Phi' = B h = \mu_0 I h / d$ | ||
| + | $ \Phi' = B h = \mu_0 I h / d $ | ||
| + | Therefore, the inductance per unit length is: | ||
| + | |||
| $L' = \frac{\Phi'}{I} = \frac{\mu_0 h}{d}$ | |||
| Substituting the numerical values | |||
| $(h = 5\ \text{mm} = 0.005\ \text{m}, d = 0.1\ \text{m}, \mu_0 = 4\pi \times 10^{-7}\ \text{H/m})$ | |||
| $L' = \frac{4\pi \times 10^{-7} \times 0.005}{0.1} = 2\pi \times 10^{-8}\ \text{H/m} \approx 6.28 \times 10^{-8}\ \text{H/m}$ | |||
| $\boxed{L' \approx 6.3 \times 10^{-8}\ \text{H/m} \; (= 63\ \text{nH/m})}$ | |||
| @@ -21,4 +28,5 @@Solution | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | |||
| + | $\boxed{L' \approx 6.3 \times 10^{-8}\ \text{H/m} \; (= 63\ \text{nH/m})}$ | ||
| @@ -1,15 +1,22 @@ | |||
| ### Statement | ### Statement | ||
| $11.3.8.$ |
$11.3.8.$ | ||
| Determine the inductance of the unit length of a two-wire line consisting of | |||
| two thin flat busbars with a width of d = 0.1 m, located at a distance of h = 5 | |||
| mm from each other. The busbars flow modulo equal but oppositely directed | |||
| currents. | |||
| ### Solution | ### Solution | ||
| For two thin conducting flat plates of width d separated by a distance" h (h \ll d)$, equal and opposite currents produce a practically uniform magnetic field in the space between them. Applying Ampère's law to a rectangular path that crosses one plate, we obtain $H = I/d $and$ B = \mu_0 I/d$ | For two thin conducting flat plates of width d separated by a distance" $h (h \ll d)$, equal and opposite currents produce a practically uniform magnetic field in the space between them. Applying Ampère's law to a rectangular path that crosses one plate, we obtain $ H = I/d $ and $ B = \mu_0 I/d $ | ||
| The magnetic flux per unit length crossing the area$ h \times 1 $between the plates is | The magnetic flux per unit length crossing the area$ h \times 1 $between the plates is | ||
| $ \Phi' = B h = \mu_0 I h / d$ |
$ \Phi' = B h = \mu_0 I h / d $ | ||
| Therefore, the inductance per unit length is: | |||
| $L' = \frac{\Phi'}{I} = \frac{\mu_0 h}{d}$ | $L' = \frac{\Phi'}{I} = \frac{\mu_0 h}{d}$ | ||
| Substituting the numerical values | Substituting the numerical values | ||
| $(h = 5\ \text{mm} = 0.005\ \text{m}, d = 0.1\ \text{m}, \mu_0 = 4\pi \times 10^{-7}\ \text{H/m})$ | $(h = 5\ \text{mm} = 0.005\ \text{m}, d = 0.1\ \text{m}, \mu_0 = 4\pi \times 10^{-7}\ \text{H/m})$ | ||
| $L' = \frac{4\pi \times 10^{-7} \times 0.005}{0.1} = 2\pi \times 10^{-8}\ \text{H/m} \approx 6.28 \times 10^{-8}\ \text{H/m}$ | $L' = \frac{4\pi \times 10^{-7} \times 0.005}{0.1} = 2\pi \times 10^{-8}\ \text{H/m} \approx 6.28 \times 10^{-8}\ \text{H/m}$ | ||
| $\boxed{L' \approx 6.3 \times 10^{-8}\ \text{H/m} \; (= 63\ \text{nH/m})}$ | $\boxed{L' \approx 6.3 \times 10^{-8}\ \text{H/m} \; (= 63\ \text{nH/m})}$ | ||
| @@ -21,4 +28,5 @@Solution | |||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | |||
| $\boxed{L' \approx 6.3 \times 10^{-8}\ \text{H/m} \; (= 63\ \text{nH/m})}$ | |||