電気と磁気(電磁気学) ~ 電磁誘導と電磁波

$$
V = – N \frac{\Delta \Phi}{\Delta t}
$$

V = – N \frac{\Delta \Phi}{\Delta t}

$$
V = vBl
$$

V = vBl

$$
V = -L \frac{\Delta I}{\Delta t}
$$

V = -L \frac{\Delta I}{\Delta t}

$$
U = \frac{1}{2} LI^2
$$

U = \frac{1}{2} LI^2

$$
V_2 = -M \frac{\Delta I_1}{\Delta t}
$$

V_2 = -M \frac{\Delta I_1}{\Delta t}

\begin{eqnarray*}
\Phi &=& BS \cos \omega t \\
\\
V &=& – \frac{\Delta \Phi}{\Delta t} = BS \omega \sin \omega t
\end{eqnarray*}

\Phi &=& BS \cos \omega t

V &=& – \frac{\Delta \Phi}{\Delta t} = BS \omega \sin \omega t

\begin{eqnarray*}
V &=& V_0 \sin \omega t \\
\\
I &=& \frac{V}{R} = \frac{V_0 \sin \omega t}{R} = I_0 \sin \omega t \\
\end{eqnarray*}

V &=& V_0 \sin \omega t

I &=& \frac{V}{R} = \frac{V_0 \sin \omega t}{R} = I_0 \sin \omega t

\begin{eqnarray*}
P &=& VI = V_0 I_0 \sin ^2 \omega t = \frac{V_0 I_0}{2} (1 – \cos 2 \omega t) \\
\\
\bar{P} &=& V_e I_e = RI_e^2 = \frac{V_e^2}{R}
\end{eqnarray*}

P &=& VI = V_0 I_0 \sin ^2 \omega t = \frac{V_0 I_0}{2} (1 – \cos 2 \omega t)

\bar{P} &=& V_e I_e = RI_e^2 = \frac{V_e^2}{R}

\begin{eqnarray*}
V_1 &=& \left | -N_1 \frac{\Delta \varPhi}{\Delta t} \right | \\
\\
V_2 &=& \left | -N_2 \frac{\Delta \varPhi}{\Delta t} \right | \\
\\
\frac{V_1}{V_2} &=& \frac{V_{1e}}{V_{2e}} = \frac{N_1}{N_2}
\end{eqnarray*}

V_1 &=& \left | -N_1 \frac{\Delta \varPhi}{\Delta t} \right |

V_2 &=& \left | -N_2 \frac{\Delta \varPhi}{\Delta t} \right |

\frac{V_1}{V_2} &=& \frac{V_{1e}}{V_{2e}} = \frac{N_1}{N_2}

$$
\frac{p}{P} = \frac{r I^2}{IV} = \frac{rI}{V} = \frac{r VI}{V^2} = \frac{rP}{V^2}
$$

\frac{p}{P} = \frac{r I^2}{IV} = \frac{rI}{V} = \frac{r VI}{V^2} = \frac{rP}{V^2}

\begin{eqnarray*}
V &=& V_0 \sin \omega t \\
\\
I &=& -\frac{V_0}{\omega L} \cos \omega t = I_0 \sin \left( \omega t – \frac{\pi}{2} \right)
\end{eqnarray*}

V &=& V_0 \sin \omega t

I &=& -\frac{V_0}{\omega L} \cos \omega t = I_0 \sin \left( \omega t – \frac{\pi}{2} \right)

$$
X_L = \omega L
$$

X_L = \omega L

\begin{eqnarray*}
V &=& V_0 \sin \omega t \\
\\
I &=& \omega CV_0 \cos \omega t = I_0 \sin \left( \omega t + \frac{\pi}{2} \right)
\end{eqnarray*}

V &=& V_0 \sin \omega t

I &=& \omega CV_0 \cos \omega t = I_0 \sin \left( \omega t + \frac{\pi}{2} \right)

$$
X_C = \frac{1}{\omega C}
$$

X_C = \frac{1}{\omega C}

\begin{eqnarray*}
P &=& VI = (V_0 \sin \omega t)(- I_0 \cos \omega t) \\
\\
&=& – \frac{V_0 I_0}{2} \sin 2 \omega t \\
\\
U &=& \frac{1}{2} LI^2 = \frac{1}{2} L(- I_0 \cos \omega t)^2 \\
\\
&=& \frac{1}{2} LI_0^2 \frac{(1+ \cos 2 \omega t)}{2}
\end{eqnarray*}

P &=& VI = (V_0 \sin \omega t)(- I_0 \cos \omega t)

&=& – \frac{V_0 I_0}{2} \sin 2 \omega t

U &=& \frac{1}{2} LI^2 = \frac{1}{2} L(- I_0 \cos \omega t)^2

&=& \frac{1}{2} LI_0^2 \frac{(1+ \cos 2 \omega t)}{2}

\begin{eqnarray*}
P &=& VI = (V_0 \sin \omega t)(I_0 \cos \omega t) \\
\\
&=& \frac{V_0 I_0}{2} \sin \omega t \\
\\
U &=& \frac{1}{2} CV^2 = \frac{1}{2} C (V_0 \sin \omega t)^2 \\
\\
&=& \frac{1}{2} CV_o^2 \frac{(1- \cos 2 \omega t)}{2}
\end{eqnarray*}

P &=& VI = (V_0 \sin \omega t)(I_0 \cos \omega t)

&=& \frac{V_0 I_0}{2} \sin \omega t

U &=& \frac{1}{2} CV^2 = \frac{1}{2} C (V_0 \sin \omega t)^2

&=& \frac{1}{2} CV_o^2 \frac{(1- \cos 2 \omega t)}{2}

\begin{eqnarray*}
I &=& I_0 \sin \omega t \\
\\
V_R &=& RI = RI_0 \sin \omega t \\
\\
V_L &=& \omega LI_0 \sin \left( \omega t + \frac{\pi}{2} \right) = \omega L I_0 \cos \omega t \\
\\
V_C &=& \frac{I_0}{\omega C} \sin \left( \omega t – \frac{\pi}{2} \right) = – \frac{I_0}{\omega C} \cos \omega t \\
\\
V &=& V_R + V_L + V_C \\
\\
V &=& RI_0 \sin \omega t + \omega LI_0 \cos \omega t + \left( -\frac{I_0}{\omega C} \cos \omega t \right) \\
\\
&=& I_0 \left \{ R \sin \omega t + \left( \omega L – \frac{1}{\omega C} \right) \cos \omega t \right \} \\
\\
&=& \sqrt{R^2 + \left( \omega L – \frac{1}{\omega C} \right) } I_0 \sin (\omega t + \theta) \\
\\
\\
V &=& ZI_0 \sin (\omega t + \theta) \ ,\ Z = \sqrt{R^2 + \left( \omega L – \frac{1}{\omega C} \right) } \ , \ \tan \theta = \frac{\omega L – \frac{1}{\omega C}}{R} \ , \ \left( -\frac{\pi}{2} \le \theta \le \frac{\pi}{2} \right)
\end{eqnarray*}

I &=& I_0 \sin \omega t

V_R &=& RI = RI_0 \sin \omega t

V_L &=& \omega LI_0 \sin \left( \omega t + \frac{\pi}{2} \right) = \omega L I_0 \cos \omega t

V_C &=& \frac{I_0}{\omega C} \sin \left( \omega t – \frac{\pi}{2} \right) = – \frac{I_0}{\omega C} \cos \omega t

V &=& V_R + V_L + V_C \\

V &=& RI_0 \sin \omega t + \omega LI_0 \cos \omega t + \left( -\frac{I_0}{\omega C} \cos \omega t \right)

&=& I_0 \left \{ R \sin \omega t + \left( \omega L – \frac{1}{\omega C} \right) \cos \omega t \right \}

&=& \sqrt{R^2 + \left( \omega L – \frac{1}{\omega C} \right) } I_0 \sin (\omega t + \theta)

V &=& ZI_0 \sin (\omega t + \theta) \ ,\ Z = \sqrt{R^2 + \left( \omega L – \frac{1}{\omega C} \right) } \ , \ \tan \theta = \frac{\omega L – \frac{1}{\omega C}}{R} \ , \ \left( -\frac{\pi}{2} \le \theta \le \frac{\pi}{2} \right)

\begin{eqnarray*}
V_e &=& ZI_e \\
\\
\bar{P} &=& RI_e^2 = Z \cos \theta \cdot \frac{V_e}{Z} \cdot I_e = V_e I_e \cos \theta
\\
\end{eqnarray*}

V_e &=& ZI_e

\bar{P} &=& RI_e^2 = Z \cos \theta \cdot \frac{V_e}{Z} \cdot I_e = V_e I_e \cos \theta

$$
f_0 = \frac{\omega _0}{2 \pi} = \frac{1}{2 \pi \sqrt{LC}}
$$

f_0 = \frac{\omega _0}{2 \pi} = \frac{1}{2 \pi \sqrt{LC}}

$$
\frac{1}{2} CV^2 + \frac{1}{2} LI^2 = \text{const.}
$$

\frac{1}{2} CV^2 + \frac{1}{2} LI^2 = \text{const.}

$$
c = \frac{1}{\sqrt{\varepsilon _0 \mu _0}}
$$

c = \frac{1}{\sqrt{\varepsilon _0 \mu _0}}