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

科目：研究所、轉學考(插大)◆普通物理學 | 年份：106年 | 選擇題數：0 | 申論題數：17

試卷資訊

所屬科目：研究所、轉學考(插大)◆普通物理學

選擇題 (0)

申論題 (17)

1. Please briefly describe the follow laws/effect/principle:

(A) Lorentz Force Law (5%)
(B) Einstein's Photoelectric Effect (5%)
(C) Heisenberg's Uncertainty Principle (5%)
(D) Lenz's Law (5%)
2. A sinusoidal electromagnetic wave of frequency 30.0 MHz travels in free space in the x direction.

(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%)
3. (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%)
[Use the symbol of h for Planck constant, m for rest mass of electron, e for electron charge]

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%)
7. Consider a uniformly wound solenoid having \(N\) turns and length \(\ell\). Assume \(\ell\) is much longer than the radius of the windings and the core of the solenoid is air. (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 \((\varepsilon_{c})\) in the solenoid if the current it carries deceased at the rate of \(dI / dt\)?
8. A capacitor of capacitance C is discharging through a resistor of resistance R. (10%)

(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?
9. Determine the electric field E caused by a spherical cloud of electrons with a volume charge density ρ = -ρ₀ for 0 ≤ R ≤ b (both ρ₀ and b are positive) and ρ = 0 for R > b in the free space (the permittivity of the free space is ε₀). (10%)

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