課程名稱︰普通物理學甲下 課程性質︰數學系大一必帶 課程教師︰黃暉理 開課學院：理學院 開課系所︰數學系 考試日期（年月日）︰2014/04/01 考試時限（分鐘）：60 試題 : 1. A copper wire with length $L_1$ and cross section A. (Suppose the conducti- vity of copper is σ.) (a) What is the resistant $r_w$ of the wire? (Show it by $L_1$, A and σ.) (9 pt.) (b) If the wire is connected to a resistance $r_2$ and a real battery having internal resistance $r_1$ and emf ξ. What are the current i and the po- tential differences across the real battery ($V_b$) and resistance $r_2$ ($V_r$)? (Show them by $r_i$ and ξ.) (27 pt.) (c) What are the powers due to the wire, the resistance of battery and the resistance $r_2$? ($P_w$, $P_b$ and $P_r$) (Show them by i and $L_2$.) (27 pt.) (d) If $L_1 = 1.0 m$, $A = 1.0 mm^2$, $r_1 = 2.9 \Omega$, $r_2 = 0.083 \Omega$ and ξ = 3.0 V. What are the answers of (a), (b) and (c)? (The resistivity of copper is $1.69 \times 10^{-8} \Omega \cdot m$.) (7 pt.) (e) Now we bend the wire to make a square loop with length $L_2$ ($S_1 \sim L_1 \gg L_2$). What is the magnitude of the magnetic field M at center due to the current of the square loop? (Show them by i and $L_2$.) (10 pt.) https://i.imgur.com/aGEuceV.png \begin{tikzpicture} \draw (8, 0.05) -- (2, 0.05) -- (2, 2) -- (-2, 2) -- (-2, -2) -- (2, -2) -- (2, -0.05) -- (8, -0.05); \draw (0, 2) node[anchor=south]{$L_2$}; \draw (2, 1) node[anchor=west]{$L_2/2$}; \draw (2, -1) node[anchor=west]{$L_2/2$}; \draw (5, 0.05) node[anchor=south]{$S_1$}; \draw (8, 0) node[anchor=west]{\ldots}; \filldraw (0, 0) circle(1pt) node[anchor=south]{$M=\ ?$}; \end{tikzpicture} 2. A particle of mass m moves along a circle in a region of uniform magnetic field of magnitude B. The particle is either a proton (charged +q) or an electron (charged -q) (you must decide which). It experiences a magnetic force of magnitude F. What are (a) the type of the particle, (b) the parti- cle's speed, (c) the radius of the circle, and (d) the period of the motion? (20 pt.) https://i.imgur.com/myLkAhV.png \begin{tikzpicture} \draw (0, 0) circle(1); \filldraw (-1, 0) circle(1pt); \draw[->] (-1, 0) -- (-1, -0.5); \draw (-1, -1) node{$\odot\vec B$}; \end{tikzpicture} -- 第01話 似乎在課堂上聽過的樣子 第02話 那真是太令人絕望了 第03話 已經沒什麼好期望了 第04話 被當、21都是存在的 第05話 怎麼可能會all pass 第06話 這考卷絕對有問題啊 第07話 你能面對真正的分數嗎 第08話 我，真是個笨蛋 第09話 這樣成績，教授絕不會讓我過的 第10話 再也不依靠考古題 第11話 最後留下的補考 第12話 我最愛的學分 --

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