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
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