106年 - 106 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2年級：普通物理#147427

(A) Lorentz Force Law (5%)

(B) Einstein's Photoelectric Effect (5%)

(C) Heisenberg's Uncertainty Principle (5%)

(D) Lenz's Law (5%)

(A) Determine the wavelength of the wave. (5%)

(B) At some point and at some instant, the electric field has its maximum value of \( 600\mathrm{N / C} \) and is directed along the y axis. Calculate the magnitude and direction of the magnetic field at this position and time. (5%)

(A) Please plot and describe how the electric generator works by electromagnetism. (5%)

(B) What is the de Brogie wavelength (λ) of an electron with a kinetic energy of K. (5%)

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

5. The voltage output of an AC source is given by the expression \( \Delta v = 141.4\sin \omega t \) where \( \Delta v \) is in volts. Find the rms current in the circuit when this source is connected to a \( 100 - \Omega \) resistor. (10%)

6. In a purely inductive AC circuit, \( L = 10.0 \, \text{mH} \) and the rms voltage is \( 314 \, \text{V} \). Calculate the inductive reactance and rms current in the circuit if the frequency is \( 50.0 \, \text{Hz} \). (10%)

(A) What is the inductance \( (L) \) of the solenoid? (The permeability in free space is \( \mu_0 \))

(B) What's the self-induced emf (ε_L) in the solenoid if the current it carries deceased at the rate of \( dI / dt \)?

(A) In terms of the time constant \( \tau = RC \), when will the charge on the capacitor be half its initial value?

(B) When will the energy stored in the capacitor be half its initial value?

(A) find \( E(R) \) for \( 0 \leq R \leq b \)

(B) find \( E(R) \) for \( R > b \)