## Induction

289. Which of the following quantities can generate an induced electric field when its change in time is non-zero?

**ANS: all of the given choices**

290. Of which of the following, the inductance value of a long cylindrical solenoid inductor is independent?

**ANS: Current**

291. emf in Faraday’s law is:

**ANS: around the boundary of the area where the magnetic flux is calculated**

292. A solenoid with length ℓ land number of turns N has a cross-sectional area A, find its self-inductance.

**ANS: $L = \frac{\mu_0 N^2 A}{l}$**

293. The energy stored in the inductor:

**ANS: is proportional to the square of the current**

294. Find the SI unit of $\frac{B^2}{2\mu_0}$.

**ANS: $J/m^3$**

295. The unit of inductance in SI system is Henry, or H, which is the equavalence of

**ANS: $T\cdot m^2 / A$**

296. A square loop is placed on the paper. A gradually decreasing magnetic field is directed into the paper. Find the induced current on the loop as

**ANS: clockwise**

297. A long straight wire and a rectangular conductive loop are both on the xy plane. The wire is placed on the left side of the loop and has a fixed current I, which flows in the positive y direction. When the wire moves to the rectangular loop, the direction of current on the loop is

**ANS: counter-clockwise**

298. LC circuit, L = 40 mH, C = 1.0 μF, find its resonance frequency.

**ANS: 800 Hz**

299. In the LC resonant circuit, the total stored energy is U. Then in a cycle, find the maximum energy that the capacitor can store.

**ANS: U**

300. A single loop encircles an area of 0.005 m$^2$ and a resistance of 25 Ω. Place it in a uniform magnetic field and perpendicular to the direction of the field. The magnetic field changes steadily from 0.60 T to 0 within 0.3 seconds. Find the magnitude of the induced current on this circuit.

**ANS: $4\times 10^{-4} A$**

301. A coil with a resistance of 1.40 Ω encircled an area of 3.50×10$^{−2}$ m$^2$, is rotating at an angular velocity of 250 rad/s with an axis perpendicular to the direction of a uniform magnetic field of 0.40 T. If the maximum induced electromotive force on this coil is 70.0 V, find the number of turns of this coil.

**ANS: 20**

302. If the current passing through the long solenoid decreases from 2.0 A to 1.8 A within 0.005 seconds, the resulting average self-induced electromotive force is 0.16 V. Calculate the self-inductance of the solenoid.

**ANS: 4mH**

303. The magnitude of the magnetic field near the current-carrying wire is 4.0 T. Find the energy density of the magnetic field at this place.

**ANS: $6.4\times 10^6 J/m^3$**

304. A coil with 200 turns and a cross-section of 8.5 cm$^2$ is placed on a piece of paper. A vertical-outward magnetic field of 0.06 T uniformly decreases to 0.02 T within 12 ms. If the resistance of the coil is 4 Ω, find the magnitude of the induced current on the coil.

**ANS: 0.14 A**

305. If the magnetic field in a long cylindrical wire of radius r0 increases uniformly, find the location from the central axis of the wire where the maximum value of the induced electric field generates.

**ANS: $r=r_0$**

306. A long solenoid with a length of 5.0 cm, a cross-section of 1.0 cm$^2$ and 300 turns, is wrapped around by the other solenoid of 180 turns. Calculate its mutual inductance.

**ANS: $1.4\times 10^{-4} H$**

307. Given an RL serial circuit, after doubling the time constant, how many times the current on it is the maximum current?

**ANS: 0.86**

308. A long straight solenoid with an inductance of 0.30 H generates a self-induced electromotive force of 1.2 V.

(A) The current increases from 0 and the increasing rate is 4.0 A/s.
(B) The current decreases from 4.0 A and the decreasing rate is 4.0 A/s.
(C\) The current increases steadily within 0.25 seconds, from 1.5 A to 2.5 A.
(D) all three given choices.
(E) none of the given choices.

**ANS: all three given choices**

309. A uniform magnetic field B is directed out of the page. A metallic wire has the shape of a square frame and is placed in the field as shown.


While the shape of the wire is steadily transformed into a circle in the same plane, the current in the frame:

**ANS: is directed clockwise**

310. As the right figure shown, MN is a fixed infinite long straight wire carrying a constant current from N to M. Now put a rectangular coil “abcd” over the wire with insulation between them and stay the coil toward the left. The current in the straight wire suddenly increases. What is the direction of magnetic force acting on the coil?


**ANS: $\rightarrow$ 向右**

311. A square loop of wire moves with a constant speed $\vec{v}$ from a field–free region, through a region of uniform $\vec{B}$ field as shown. Which of the five graphs correctly shows the induced current I in the loop as a function of time t?

如圖, 有一方形金屬線圈以定速度進入一穩定均勻磁場 $\vec{B}$ 區域, 再維持同樣速度離開。請問在金屬線圈上的感應電流 I 與時間 t 的函數圖, 下列何者正確?


**ANS: **

312. The drawing shows a copper wire of negligible resistance bent into a circular shape with a radius of r. The radial section BC is fixed in place, while the copper bar AC sweeps around at an angular speed of ω. The bar makes electrical contact with the wire at all times. The wire and the bar have negligible resistance. A uniform magnetic exists everywhere, is perpendicular to the plane of the circle, and has a magnitude of B. Which of the following shows the magnitude of the current I as a function of θ?


**ANS: TBA**

313. A uniform and constant magnetic field B is directed into the page within a rectangular region as shown in the figure.


A wire in the shape of a quarter-circle is rotated at a constant angular velocity about an axis A. Which of the following graph represents the emf E induced in the wire as a function of time?

**ANS:**


314. A rectangular loop of wire with dimensions shown is coplanar with a long wire carrying current I. The distance between the wire and the left side of the loop is r. The loop is pulled to the right as indicated. What are the directions of the induced current in the loop and the magnetic forces on the left and the right sides of the loop as the loop is pulled?


**ANS: Induced Current: Clockwise; Force on Left Side: To the right**

315. A long straight wire is in the plane of a rectangular conducting loop


The straight wire carries an increasing current in the direction shown. The current in the rectangle is:

**ANS: counterclockwise**

316. A long, straight wire carries a steady current I.


A rectangular conducting loop lies in the same plane as the wire, with two sides parallel to the wire and two sides perpendicular. Suppose the loop is pushed toward the wire as shown. Given the direction of I, the induced current in the loop is

**ANS: counterclockwise.**

317. The bar magnet shown in the figure is moved completely through the loop. Which of the following is a true statement about the direction of the current flow between the two points a and b in the circuit?


**ANS: Current flows from a to b as the magnet enters the loop and from b to a as the magnet leaves the loop.**

318. A magnet is held between two conductive rings that are attached to a friction-negligible rail by two insulators (They can move freely to the left and right).


If we move the magnet to the left what will happen to the rings?

**ANS: “A” will move left and “B” will move right**

319. 如右圖兩平行無限長直導線通入同向之相等電流，其間有一矩形導線線圈， 三者同一平面。如線圈等速向左平移，問線圈中感應電流方向?


**ANS: 逆時針方向**

320. 有一長度為ℓ 之螺線管電感元件，截面為a，其上繞有N 圈匝數。若通過電感器的電流I 以+di/dt之變化率遞增，下列何者正確？

**ANS: 電感值L 與di/dt無關。**

321. The quantity $\frac{1}{2\mu_0}\vec{B^2}$ has the meaning of:

**ANS: magnetic energy per unit volume**

322. Which of the following statement is NOT correct?

**ANS: A time-varying current can induce a steady magnetic field.**

323. In the R-L circuit, a DC battery $\varepsilon$ , the switch S is connected for a long time.


Now, the switch is suddenly opened (disconnected). Just after the switch is opened, what is the potential difference across the inductor L?

**ANS: $\frac{R_1 + R_2}{R_2}\varepsilon$**

324. As figure shown, the big coil is suddenly connected to a current.
如附圖，大環突然產生電流，則大小環之間的作用力方向如何？


Find the direction of the interaction force between two coils.

**ANS: It is repulsive**

325. 冷次定律是下列哪一項的必然結果？

**ANS: 能量守恆**

326. 如圖，長ℓ = 20 cm 之金屬棒在理想、導體製成的U 形光滑軌道上，以0.8 m/s 的速度向右移動，金屬棒的電阻為0.25 Ω 。若外加磁場大小為0.5 T, 則通過金屬棒的電流大小及方向


**ANS: 0.32 A 向下**

327. There is a current I passing through an inductor with inductance L. How much energy is stored in the inductor?

**ANS: $\frac{1}{2}LI^2$**

328. Electric fields produced by changing magnetic fields

**ANS: are non-conservative**

329. A small magnet that is suspended by a thread is placed near the end of a solenoid carrying a direct current i.


What happens to the magnet as the soft iron core is inserted into the solenoid?

**ANS: The magnet will swing to the right.**

330. 有一電路元件，可將機械能轉換為電能。請問下列何者為其正確名稱？

**ANS: 發電機**

331. 如圖所示，一封閉圓形金屬線圈甲內部有一絕緣體圓環乙，且圓環上均勻分布電荷。小米發現在圓環乙轉動的狀態下， 線圈甲產生順時針方向的感應電流I. 關於『圓環乙上電荷電性』與『圓環乙轉動情形』，下列敘述何者正確？


**ANS: 負電荷，逆時針旋轉，越轉越慢**

332. A small coil lies inside a large coil. The two coils are horizontal and concentric as shown. The large coil carries a constant clockwise current.


**ANS: clockwise, attraction**

333. The principle or law that says “an induced emf in a closed circuit loop produces a current whose magnetic field opposes further change of magnetic flux” is credited to

**ANS: Lenz**

334. A long metal bar, 30.0 cm in length , is aligned along a north-south line and moves eastwards at a speed of 10.0 m/s. A uniform magnetic field of 4.00 T points downwards. If the south end of the bar has a potential of 0 V, the induced potential at the north end of the bar is

**ANS: +12V**

335. The figure shows three metal loops labeled A, B, and C heading towards a region where a uniform static magnetic field exists. The loops move with the same constant velocity and all have the same resistance. Their relative sizes are indicated by the background grid. As they enter the magnetic field the loops will have an induced electric current in them. For which loop will the current be the greatest?


**ANS: C**

336. Inductors of value L, 2L and 3L are connected in series. What is the equivalent inductance?

**ANS: 6L**

337. The intensity of an EM wave propagating in vacuum is given as I. If the amplitude of the electric field component of this wave is doubled, what would be the new intensity?

**ANS: 4I**

338. Inductors of value L, 2L and 3L are connected in parallel. What is the equivalent inductance?

**ANS: 6L/11**

339. There are no currents and permanent magnets present, but there is a non-zero magnetic field. What else must be present?

**ANS: changing electric field**

340. A circular loop of wire lies in the plane of the paper. An increasing magnetic field points out of the paper. What is the direction of the induced current in the loop?

**ANS: clockwise**

#### Added Questions

1. The magnetic energy stored in an inductor is

A. proportional to the square of the magnetic field of the inductor.

B. both of the two given choices

C. proportional to the square of the current through the inductor.

**ANS: both of the two given choices**

2. A resistor R and an inductor L are connected in series to a battery, which is switched on at t = 0. The current in the circuit is time-dependent. If we repeat the experiment with a resistor of resistance 5R, the time constant

**ANS: decreases by a factor of 5**

3. 一個由 50 匝緊纏在一起的長方形線圈，長度為 0.25 (m), 寬度為 0.12 (m), 強度為 2.0 (Tesla) 的均勻磁場中轉動。 如線圈面原與磁場成 30$^\circ$ 角，在 0.10 秒內轉成線圈面垂直於磁場， 且轉軸與磁場方向垂直，則線圈的平均感應電動勢約為若干伏特？

**ANS: 15 (Volt)**

4. A magnet moves inside a coil. Consider the following factors; which of the following(s) can affect the emf induced in the coil?

I. strength of the magnet
II. number of turns in the coil
III. speed at which the magnet moves

**ANS: I, II, III**

5. Which is TRUE?

a. both of the two given choices
b. neither of the two given choices
c. The induced electric field is conservative.
d. The field lines of an induced electric field form closed loops.

**ANS: The field lines of an induced electric field form closed loops**

6. Two current-carrying coils of wire are in close proximity. It is suggested that we can change the mutual inductance of the pair by:

1. “Changing the relative positions of the coils.”
2. “Changing the currents.”
3. “Increasing the number of turns in one of the coils.”

Which of the following choices is correct and better than others?

**ANS: Only two of the three given methods are correct**

7. 下列何者產生磁場？

**ANS: 帶電荷的運動物體 “a moving object with electric charge” and “a stationary conductor carrying electric current”.**

8. 在圖 OQ23.12 中，開關長時間保持在位置 a. 然後突然快速切向位置 b.
在開關切換後的瞬間，將四個電路元件上的電壓，從最大排列到最小。

**ANS: $ΔV_L>ΔV_{1200Ω}> 12.0 V >ΔV_{12Ω}$**

9. 將一扁平線圈置於均勻同向磁場中，磁場指向 y 方向。此線圈平面置在下列各選項， 何者使此線圈有最大磁通量？

**ANS: 線圈面在 xz 平面**

10. 當發電機線圈的轉速加倍時，感應電動勢的振幅發生以下何種變化？

**ANS: 變成原來的兩倍**

11. 一矩形導體線圈放在一長直導線旁，導線承載電流 I 如圖 OQ23.5 所示。


如 I 隨時間漸減，線圈中感應電流會如何？

**ANS: 電流為順時針方向**

12. 如圖 OQ23.10 所示，一長導體棒在平行軌道上以速度 v 向右等速運動，軌道區域中有一均勻同向磁場 B 垂直軌道面衝出紙面


下列各項敘述何者正確?

**ANS: 迴路中的感應電流為順時針方向**

13. 兩線圈彼此靠近放置，如圖 OQ23.15 所示。


左邊線圈連接到電池和開關，右邊線圈連接一電阻器。開關按下的數秒之後，求電阻上的電流方向。

**ANS: 沒有電流**

14. 如果電感器中的電流加倍，則電感器中儲存的能量會變成幾倍？

**ANS: 4**

15. 下列關於電磁感應的敘述，何者正確？

**ANS:
質子減速度運動時，會產生電磁波
磁通量隨時間變化時，會產生電場**

16. 將一扁平線圈置於均勻同向磁場中，磁場指向 y 方向。此線圈平面置在下列各選項，何者使此線圈之磁通量為 0?

**ANS: 線圈面在 xy 平面或線圈面在 yz 平面，皆可**

17. 一半徑逐漸增大的線圈上的穿透磁通量對時間的函數圖，Figure OQ23.1. 前述時間內, 線圈同時旋轉一圈半。 然後關閉外加磁場。


比較 A, B, C, D, E 五個時刻所產生的線圈感應電動勢，依序排列，由最大正值至最大負值。 下列何者正確?

**ANS: E > A > B = D = 0 > C**

18. 兩個矩形導線迴路置於同一平面內，如圖 OQ23.17 所示。


如外側迴路電流 I 為逆時針方向並且隨著時間漸增，關於內側迴路感應電流，下列各項敘述何者『正確』？

**ANS: 順時針、內側迴路感應電流大小取決於兩個迴路的幾何因素**

19. 如圖 OQ23.13 所示，條形小磁鐵以垂直方向固定在一位於水平面的導線迴路正上方。


磁鐵的 S 極朝向迴路。 磁鐵落下後，從上方觀察，關於迴路中的感應電流， 下列敘述何者『正確』？

**ANS: 磁鐵向迴路落下時，感應電流為順時針方向**

## EMWave

341. 哪位科學家首先實驗證實了電磁波的發射/接收理論？

**ANS: 赫茲**

342. 馬克斯威爾將之前科學家所提出的四個電場/磁場關係式進行修正和彙整推廣，請問他修正是哪個方程式？

**ANS: 安培定律**

343. 若下列四個方程式是真空情況下的 Maxwell 方程式


**ANS: 四個方程式皆正確**

344. 若真空內有沿 z 軸移動的電磁波, 則下列何者不可能是 Maxwell 方程式所推導出的電磁波波動方程式？

**ANS: $\frac{\partial^2E_z}{\partial z^2}=\mu_0\varepsilon_0\frac{\partial^2E_z}{\partial t^2}$**

345. 若真空內有沿 z 軸移動的電磁波，則其波速 c 為？

**ANS: $\frac{1}{\sqrt{\mu_0\varepsilon_0}}$**

346. 下列關於真空中電磁波的Poynting vector $\vec{S}$ 之敘述，何者錯誤？

**ANS: Poynting vector 單位為功率單位(例如 Watt)**

347. 下列關於真空中電磁波的 Poynting vector 大小(S)的敘述，何者正確？

**ANS: 以上皆正確**

348. 若真空中電磁波的電場 $E = E_0 \sin(kx − ωt)$，求其平均 Poynting vector 強度？

**ANS: $\frac{1}{2}c\varepsilon_0E^2_0$**

349. 具有均勻強度的雷射光束，其平均功率為 5.1 mW, 光束半徑為 1.3 mm。 此光束垂直照射在完全反射面上時，將造成多少光壓？

**ANS: $2.0\times10^{-5}$ Pa**

350. 下列何者是真空中沿 y 軸方向偏極，且朝 z 軸移動之電磁波的電場表示式？

**ANS: $\vec{E} = E_0 \sin(kz − ωt)\hat{j}$**

351. 如果真空中電磁波的波數(wave number) k = 300 rad/m, 則其角頻率 ω=？

**ANS: $9\times10^{10}$ rad/s**

352. 若真空中電磁波的電場振幅 E0 與磁場振幅 B0 之間的關係為何？(c=光速)

**ANS: $\frac{E_0}{B_0}=c$**

353. 下列關於氫原子發射光譜的敘述，何者錯誤？

(A) 光譜內各種顏色之電磁波的發射機制和彩虹原理類似
(B) 在可見光區域，光譜只呈現出某些特定波長的電磁波
(C\) 在可見光區域，光譜頻率具有連續分布特性
(D) 讓氫氣通過高壓電弧就可產生此光譜
(E) 光譜不但呈現可見光區域電磁波， 也有非可見光區域的電磁波

**ANS: 在可見光區域，光譜頻率具有連續分布特性**

354. 下列敘述，何者錯誤？

(A) 可見光波長範圍約為 400 nm 至 700 nm
(B) 波長 800 nm 電磁波屬於紫外線區域
(C\) X 光波長約在 1 nm 附近
(D) 微波爐內大部分電磁波的波長大小約數個 cm附近
(E) 物體溫度越高，發射出的電磁波波長越小.

**ANS: 波長 800 nm 電磁波屬於紫外線區域**

355. 下列何種電磁波在真空內的傳波速率最快：

**ANS: 以上所有電磁波的速率皆相同**

356. 我們周圍環境中的無線電波與可見光之不同處是，無線電波

**ANS: 頻率較低**

357. 關於馬克斯威爾所提出的位移電流(displacement current)大小，下列敘述何者正確？

**ANS: 與 $d\Phi_E/dt$ 成正比**

358. 半徑 R 之理想圓形平板電容器在充電過程中，何處的感應磁場最大？

**ANS: 圓形板邊緣處 (r = R)**

359. 以固定電流 i = 3.0 mA 將半徑 3 cm 之理想圓形平板電容器充電時, 求此電容器邊緣處的感應磁場？

**ANS: $2\times10^{-8}$ T**

360. 如果電磁波發射源為一個很小的點波源，則可將其電磁波波形視為

**ANS: 距波源極遠處是平面波、極近處是球面波**

361. 以下馬克斯威爾方程式，何者形式不適用於真空狀態？

**ANS: $\oint_C \vec{E} \ \cdot d\vec{a} = \frac{q_{enc}}{\varepsilon_0}$**

362. A changing electric flux generates

**ANS: magnetic field**

363. Which one of the following quantities of electromagnetism is linearly proportional to “displacement current”?

**ANS: The time changing rate of electric flux**

364. 如附圖所示，自南向北前進的電磁波於某瞬間其磁場方向朝東，則其電場方向為何？


**ANS: 向上**

365. 圖中表示出在某一瞬間某一定點的電磁波之電場圖，波往$-\hat{z}$ 方向輸送能量，則在此瞬間該點的磁場方向為何？

**ANS: $+\hat{x}$**

366. An electromagnetic wave is propagating in vacuum in the positive z direction. At an instant when its magnetic field B at a certain position is in the positive x direction and getting stronger, what happens to its electric field E at that same position?

**ANS: E is in the negative y direction and getting stronger**

367. Which of the following radiation types has the longest wavelength?

**ANS: Radio waves**

368. In which of the following lists are the parts of the electromagnetic spectrum ordered correctly from shortest wavelength (at the top) to longest wavelength (at the bottom)?

**ANS: X-ray, ultraviolet, visible, infrared, radio**

369. Which of the following is NOT true for electromagnetic waves

**ANS: they have no momentum**

370. Greenhouse “warming” is caused by an atmosphere which is

**ANS: transparent to visible light but opaque to I.R. light**

371. Of the following types of waves, which type travels at the greatest speed through vacuum?

**ANS: None of the above; all these waves would travel at the same speed**

372. 潛艇探測水中目標常用的工具是聲納，聲納向水中目標發射超聲波，超聲波被目標反射後又被潛艇的聲納 系統所接收。測出發送到接收經過的時間就可知潛艇和目標之間的距離。但是在另一方面，雷達站探測空 中的目標則常用電磁波，為什麼潛艇要用超聲波?

**ANS: 因為電磁波在水中很容易衰減，傳播距離不遠，而聲波在水中可傳播較遠的距離**

373. 電磁波會產生偏極現象，聲波不會。請問下列解釋何者正確？

**ANS: 聲波為縱波，電磁波為橫波。**

374. A vertically polarized plane wave (an AM radio wave) is emitted by a radio antenna and travels across flat ground. Which of the following could describe the direction of the magnetic field component of the wave?

**ANS: Parallel to the ground and perpendicular to the direction of propagation**

375. 愛因斯坦提出光子的概念，有關光強度的解釋，下列敘述何者正確？

**ANS: 光強度愈強表示每單位時間內通過單位截面積的光子數目愈多**

376. What is the unit of Poynting vector?

**ANS: kg/s${^3}$**

377. If there were only one transmitter, and you were separated from this transmitter by the many tall buildings to be found in downtown Toronto, spaced about 30 m apart on average, with which of the following would you be most likely to experience dead spots (places with very poor or no reception)?

**ANS: cell phones (frequency 1000 MHz)**

378. A capacitor has been charged to a constant potential V . The displacement current between its plates

**ANS: is equal to the current that was required to charge up the capacitor**

## AC circuit

379. 在串聯 RL, RC 或 RLC 基本交流電路實驗時，使用示波器觀察利薩如圖形，其目的為測量

**ANS: 以上皆非**

380. 在串聯 RL, RC 或 RLC 基本交流電路實驗時，使用示波器觀察利薩如圖形，若利薩如圖形呈一斜直線，則電路的阻抗值Z為

**ANS: 最小值**

381. 交流電源驅動串聯 RLC 電路，使用 R = 200 Ω, C = 4.7µF, L = 10 mH, 當頻率為從 730 Hz 變為 3.3 kHz 時，容抗的大小變化為

**ANS: 變小**

382. 進行 RLC 基本交流電路實驗時，沒有使用到下列那一項儀器

**ANS: 直流電源供應器**

383. 電感器的感抗 XL 為何？

**ANS: $2πfL$**

384. 電感器感抗 XL 的單位為何？

**ANS: 歐姆**

385. 電容器的容抗 XC 為何？

**ANS: $\frac{1}{2\pi fC}$**

386. 電容器容抗 XC 的單位為何？

**ANS: 歐姆**

387. 如右圖，若線路中之電源電流函數為 $I(t) = I_{max} \sin ωt$, 則下列敘述何者正確？


**ANS: 電源電壓為 $V_i(t) = V_R(t) + V_L(t)+V_c(t)$**

388. 如右圖 AC 電路中總電阻應為


**ANS: $\sqrt{R^2 + (X_L - X_C)^2}$**

389. 如右圖，若線路中之電源電流函數為 $I(t) = I_{max} \sin ωt$, 以三用電表測量電源電壓及電路電流這兩個數據可以推算出下列那個物理量


**ANS: Z**

390. 如下圖的裝置，可以測量下列那些物理量？


i. 電源電壓函數
ii. 電源電流函數
iii. 電阻電壓函數
iv. 電源電壓與電流之相位差

**ANS: i, iii, iv**

391. 峰值 V 之弦波交流電壓的方均根值大小為?

**ANS: 0.707 V**

392. 峰值 V 之三角形波交流電壓的方均根值大小為?

**ANS: 0.578 V**

393. 峰值 V 之方形波交流電壓的方均根值大小為?

**ANS: 1.00 V**

394. 峰值 V 之鋸齒波交流電壓的方均根值大小為?

**ANS: 0.578 V**

395. 在串聯 RLC 基本交流電路實驗時，電感器 L 本身的電壓和電流比較相位：

**ANS: 電壓相位超前電流相位**

396. 在串聯 RLC 基本交流電路實驗時，電容器 C 本身的電壓和電流比較相位：

**ANS: 電壓相位落後電流相位**

397. 在串聯 RLC 基本交流電路實驗時，電阻器 R 本身的電壓和電流比較相位:

**ANS: 電壓相位與電流相位相同**

398. 在串聯 RLC 基本交流電路實驗時，訊號產生器之驅動電壓和電流比較相位:

**ANS: 電壓相位與電流相位關係必須由 RLC 元件值決定超前或落後**

## Wave Optics

399. 在雙狹縫干涉實驗中，屏幕上兩相鄰亮紋的間距為 1.50 mm. 假設狹縫寬度遠小於波長，兩狹縫間距為 0.150 mm, 且屏幕與狹縫相距 50 cm, 則光源的波長為多少 nm?

**ANS: 450**

400. 單狹縫繞射實驗中，若縫繞圖形之第二暗紋中心 (m = 2) 發生在 θ = 40$^\circ$, 求狹縫寬度與波長之比例？

**ANS: 3.1**

401. 在雙狹縫干涉實驗中，狹縫寬度為 a, 而雙狹縫距離為 d. 如果干涉圖形之第 5 暗紋 (m=4) 與繞射圖形之第 2 暗紋 (m′=2) 重合, 則 d/a 之比例？

**ANS: 9/4**

402. 有一繞射光柵，3 cm 內有 1.31 ×104 條刻紋, 以波長 589 nm 和 589.59 nm 的兩種黃色光波正向入射光柵, 則此兩種波長光波之第二階 (m = 2) 繞射光的夾角為幾度?

**ANS: 0.0344**

403. 以波長 656.3 nm 之光波正向入射光柵， 在其後方的 31.67$^\circ$ 和 51.95$^\circ$ 出現繞射光點, 求光柵每公尺有多少條狹縫或刻痕？

**ANS: 400,000**

404. 在楊氏雙狹縫實驗中，若波長為 600 nm 之光波產生的第 5 暗紋, 與另一單色光波產生的第 6 亮紋 (中央亮紋不計入) 重疊, 則另一單色光波的波長是多少 nm?

**ANS: 450**

405. 折射率 n = 1.52 的鏡片表面鍍了 n = 1.38 的抗反射光學薄膜, 假設入射光波長 λ = 600 nm, 請問此薄膜的最小厚度為多少才可以消除反射光？

**ANS: 109 nm**

406. 波長 λ = 652 nm 的單色光垂直入射並通過一光柵, 其第一階繞射光的角度為 θ = 18.3$^\circ$，請問光柵上的狹縫間隔(或狹縫週期)？

**ANS: 2.08 µm**

407. 假設你嘗試在一玻璃表面上放置一透明薄膜，使得波長 λ = 570 nm 之光波的反射減至最小。如果薄膜和玻璃的折射率分別是 1.30 和 1.50, 請問此薄膜的最小厚度是多少？

**ANS: 110 nm**

408. 一束強度為 $I_0$ 的平面(或線性)偏振光垂直入射偏振片, 若光之偏振方向與偏振片之穿透軸夾 45$^\circ$，則穿透光強度為：

**ANS: $\frac{I_0}{2}$**

409. 波長 710 nm 之單頻光經過寬度 8.50 ×10$^{−4}$ mm 的單狹縫, 在其後方 4.0 m 的屏幕上形成繞射圖形。則中央亮紋的寬度為：

**ANS: 6.68 mm**

410. 波長 575 nm 之光波通過寬度 a= 0.25 mm 之單狹縫，因而產生繞射圖形， 則 m = 2 與 m = −2 的兩條暗紋之夾角為：

**ANS: $0.52^\circ$**

411. 假設單狹縫繞射圖形的中央亮紋之寬度 ∆x = 3.1 mm, 狹縫至屏幕距離為 0.64 m, 而狹縫寬度為0.28 mm, 則入射之光波長 λ 為：

**ANS: 680 nm**

412. 光由空氣中入射至折射率 n = 1.62 的薄玻璃片, 其表面反射光為線性(或平面)偏振光，則入射角為：

**ANS: $58^\circ$**

413. 波長 600 nm 的光進入相距 0.08 mm 的雙狹縫，則在狹縫後方 2.0 m 處之屏幕上, m = 1 亮紋與 m = −1 亮紋之間相距多遠？

**ANS: 3.0 cm**

414. 波長 600 nm 及 400 nm 的光進入相距 0.08 mm 的雙狹縫, 則在距狹縫 2.0 m 處之屏上形成干涉圖案, 則波長 600 nm 之第幾級亮紋恰落在波長 400 nm 之第 3 級亮紋上?

**ANS: 2**

415. 油膜 (n = 1.25) 浮在水 (n = 1.33)上, 若 500 nm 的光垂直照射會產生強烈反射，此油膜之最小厚度是多少？

**ANS: 200 nm**

416. 波長 600 nm 的光照射在寬 0.01 mm 之單狹縫上, 則在距狹縫 60 cm 處之屏幕上所呈現之中央亮紋之寬度是多少？

**ANS: 7.2cm**

417. 雙狹縫繞射圖案中，若兩狹縫之間隔是縫寬的 5 倍, 則在中央亮紋內有多少干涉亮紋？

**ANS: 9**

418. 未偏振光透過三片偏振板，其中第二片偏振板是由第一片偏振板轉 30$^\circ$, 而第三片偏振板是由第二片偏振板轉 30$^\circ$, 則最後透射光的強度是原來之光的強度百分比是多少？

**ANS: 28%**

419. 中午時, 空中的紫外線強度與早晨時的紫外線強度之間的強弱關係為何？

**ANS: 中午的紫外線強度較強**

420. 電場只在固定方向振動的光線稱為

**ANS: 偏振光**

421. 產生穩定可見雙狹縫干涉圖形的光源條件為:

**ANS: 偏振光**

422. 下列敘述的雷射光特性, 何者有誤？

**ANS: 為偏振光**

423. 如圖有兩組雙狹縫光線干涉圖形. 已知 A, B 兩組之雙狹縫間隔 d 相等. 左方 A 組光波頻率, $f_A$, 與右方 B 組光波頻率, $f_B$, 何者較高？何者較低？


**ANS: $f_A > f_B$**