104年 - 104 國立臺北大學_學士班曁進修學士班轉學生招生考試試題_電機工程學系學士班2年級：普通物理#147487

1. Please describe the differences of energy-band gap patterns among \( ① \) insulators, \( ② \) semiconductor, and \( ③ \) metals. \( (5\%) \)

2. Find the electric field (E) due to an infinite plane of positive charge with uniform surface charge density \( (\rho) \) in free space. \( (5\%) \) [Note: the permittity of free space is \( \tau_0 \)]

3. Please explain the Einstein's Photoelectric effect. (5%)

4. What's the Heisenberg's Uncertainty Principle? (5%)

5. What is the de Brogie wavelength of an electron with a kinetic energy of \( 200\mathrm{eV} \). (10%) [Note: use the symbol of \( h \) for Planck constant, \( m \) for rest mass of electron, \( e \) for electron charge]

6. Please write down the Maxwell's (four) equations in integral form. \( (10\%) \)

① What is the potential difference across the capacitor?

② If the battery is disconnected from the circuit, over what time interval does the capacitor discharge to one-tenth its initial voltage?

8. A solenoid has length \( L = 1\mathrm{m} \) and inner diameter \( d = 3\mathrm{m} \), and it carries a current \( i = 5\mathrm{A} \). It consists of 4 close-packed layers, each with 250 turns along length \( L \). What is B at its center? (10%) [Note: \( \mu_0 = 4\pi \times 10^{-7}\mathrm{T - m / A} \)] 

9. The resistor \( R \) in Figure below receives \( 20.0\mathrm{W} \) of power. Determine the value of \( R \). (10%)

10. An electric heater is constructed by applying a potential difference of \( 120\mathrm{V} \) across a Nichrome wire that has a total resistance of \( 12\Omega \). Find \( \text{①} \) the current carried by the wire \( \text{②} \) the power rating of the heater. (10%)

11. An LED is constructed from a \( p - n \) junction based on a certain compound semiconductor whose energy gap is \( 2.0\mathrm{eV} \). What is the wavelength of the emitted light? (10%) [Note: electron charge, \( e = 1.6\times 10^{-19}\mathrm{J / eV} \). Planck constant, \( h = 6.6\times 10^{-34}\mathrm{J}\cdot \mathrm{sec} \). Speed of light, \( c = 3\times 10^{8}\mathrm{m / sec} \)]

12. A \( 6.0\mathrm{kg} \) block initially at rest is pulled to the right along a frictionless, horizontal surface by a constant horizontal force of 9N. Find the block's speed after it has moved \( 3.0\mathrm{m} \). (10%)