---
# System prepended metadata

title: 6月25日檢討
tags: [高中物理]

---

# 6月25日檢討
###### tags: `高中物理`
## EZ100
### 1
![](https://i.imgur.com/G1zjRXh.jpg)
$\theta=\omega t$ 為圈面**法線**方向與磁場的夾角
$\alpha=90^\circ-\theta$ 為圈面方向與磁場的夾角
磁通量 $\Phi_B(t)=BA\cos\theta=BA\cos(\omega t)$
感應電動勢 $\mathcal{E}(t)=-N\dfrac{\text{d}\Phi_B(t)}{\text{d}t}=-N\dfrac{\text{d}}{\text{d}t}\left[BA\cos(\omega t)\right]=NBA\omega\sin(\omega t)$

- (A)(B) $\alpha=60^\circ$、$\theta=30^\circ$ 
    $\implies\Phi_B=BA\cos 30^\circ=\dfrac{\sqrt{3}BA}{2}$、$\mathcal{E}=NBA\omega\sin 30^\circ=\dfrac{NBA\omega}{2}$
- (C\) $\mathcal{E}(t)$ 最大值為 $NBA\omega$
- (D) $\left|\overline{\mathcal{E}}\right|=N\dfrac{\Delta \Phi_B}{\Delta t}=N\dfrac{BA-0}{T/4}=\dfrac{NBA}{\pi/2\omega}$ 
- (E) 感應電動勢 $\mathcal{E}(t)$ 方向發生變化代表磁通量 $\Phi_B$ 經過極值，即圈面與磁場垂直時。
### 2
![](https://i.imgur.com/uIHs7pY.png)
### 3
![](https://i.imgur.com/b5nPh1W.jpg)
### 4
![](https://i.imgur.com/yVw11o0.png)
$|\mathcal{E}|=\dfrac{\text{d}\Phi_B}{\text{d}t}=\dfrac{\text{d}}{\text{d}t}(BA)=\dfrac{\text{d}}{\text{d}t}(\beta t \pi r^2)=\beta\pi r^2$
### 5
![](https://i.imgur.com/OcJiimA.jpg)
### 6
![](https://i.imgur.com/8zmXoc9.jpg)
1. $|\Phi_B(0)|=B(0)A(0)=\boxed{B_0\ell d}$
2. 
    $B(t)=B_0(1-\alpha t)=B_0-\alpha B_0t,\quad B'(t)=-\alpha B_0$
    $A(t)=\ell x(t),\quad A'(t)=\ell x'(t)=\ell v(t),\quad A'(0)=\ell v(0)=0$
    $\begin{align}|\mathcal{E}(0)|&=\left|\Phi_B'(0)\right|=\left|(BA)'\right|_{t=0}=\left|AB'+BA'\right|_{t=0}\\&=\left|A(0)B'(0)+B(0)A'(0)\right|=|\ell d\times(-\alpha B_0)+B_0\times 0|\\&=\boxed{\ell d \alpha B_0}\end{align}$
3. 感應電流方向：順時針、由B到A
    感應電流量值 $I(0)=\dfrac{|\mathcal{E}(0)|}{R}=\boxed{\dfrac{\ell d \alpha B_0}{R}}$
4. 加速度量值 $a(0)=\dfrac{F(0)}{m}=\dfrac{\ell B(0)I(0)}{m}=\dfrac{\ell B_0\frac{\ell d \alpha B_0}{R}}{m}=\boxed{\dfrac{\ell^2B_0^2\alpha d}{mR}}$
### 7
![](https://i.imgur.com/65n3I0V.jpg)
$v^2=0^2+2ad\implies v=\sqrt{2ad}$
$I=\dfrac{\mathcal{E}}{R}=\dfrac{B\ell}{R}\dfrac{\text{d}x}{\text{d}t}=\dfrac{B\ell v}{R}=\boxed{\dfrac{B\ell \sqrt{ad}}{R}}$


## 歷屆107 物理
### 第9題
![](https://i.imgur.com/ZATx79T.png)
### 第13題
![](https://i.imgur.com/SOBxEw1.png)
![](https://i.imgur.com/7cveCg3.png)
### 第16題
![](https://i.imgur.com/c0Xqpq9.png)
![](https://i.imgur.com/1OBdIhY.png)
### 非選擇一
![](https://i.imgur.com/LKzN36l.png)
![](https://i.imgur.com/rXqCf8v.png)

## 歷屆107 化學
### 第8題
![](https://i.imgur.com/IP8zQJb.png)

