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Physics: waves, electricity and magnetism: board exam questions with solutions

On the ECE exam under General Engineering and Applied Sciences (GEAS) and the REE exam under Engineering Sciences and Allied Subjects (ESAS). Try each question before you open its solution, then practise with fresh numbers below: 2 computed question types on this topic.

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Questions

1. What is the free-space wavelength of a 100 MHz FM broadcast signal?

  1. 30 m
  2. 0.3 m
  3. 300 m
  4. 3 m
Show the answer and solution

Answer: D. 3 m

λ = c/f = (3×10⁸)/(100×10⁶) = 3 m.

2. Point charges of 2 µC and 3 µC are 0.1 m apart in air. What force acts between them? (k = 8.99×10⁹ N·m²/C²)

  1. 5.39 N
  2. 0.54 N
  3. 53.9 N
  4. 0.054 N
Show the answer and solution

Answer: A. 5.39 N

F = kq₁q₂/r² = 8.99×10⁹ × 2×10⁻⁶ × 3×10⁻⁶/0.01 = 5.39 N. The charges repel.

3. A 0.5 m straight conductor carries 10 A at right angles to a uniform 0.2 T magnetic field. What force acts on it?

  1. 0.1 N
  2. 1 N
  3. 10 N
  4. 25 N
Show the answer and solution

Answer: B. 1 N

F = BIL sin 90° = 0.2 × 10 × 0.5 = 1 N.

4. What is the magnetic flux density 5 cm from a long straight wire carrying 20 A in air?

  1. 40 µT
  2. 800 µT
  3. 8 µT
  4. 80 µT
Show the answer and solution

Answer: D. 80 µT

B = µ₀I/(2πr) = (4π×10⁻⁷ × 20)/(2π × 0.05) = 8×10⁻⁵ T = 80 µT.

5. A parallel-plate capacitor has 0.01 m² plates separated by 1 mm of dielectric with εr = 4. Find its capacitance.

  1. 88.5 pF
  2. 35.4 pF
  3. 354 pF
  4. 3.54 nF
Show the answer and solution

Answer: C. 354 pF

C = ε₀εrA/d = 8.854×10⁻¹² × 4 × 0.01/0.001 = 3.54×10⁻¹⁰ F = 354 pF.

6. Light passes from air into glass (n = 1.5) at an angle of incidence of 30°. What is the angle of refraction?

  1. 45.00°
  2. 19.47°
  3. 20.00°
  4. 48.59°
Show the answer and solution

Answer: B. 19.47°

By Snell's law, sin θ₂ = sin 30°/1.5 = 0.3333, so θ₂ = 19.47°.

7. Which statement about a plane electromagnetic wave in vacuum is correct?

  1. E and B are perpendicular to each other and to the direction of travel
  2. E is parallel to the direction of travel
  3. E and B are parallel to each other
  4. It needs a medium to propagate
Show the answer and solution

Answer: A. E and B are perpendicular to each other and to the direction of travel

EM waves are transverse: E ⊥ B ⊥ the propagation direction. They travel at c in vacuum and need no medium.

8. An ambulance siren sounds at 800 Hz. It approaches a stationary listener at 25 m/s, and the speed of sound is 343 m/s. What frequency does the listener hear?

  1. 858.3 Hz
  2. 745.8 Hz
  3. 862.9 Hz
  4. 825.0 Hz
Show the answer and solution

Answer: C. 862.9 Hz

For a moving source and stationary observer, f′ = f·v/(v − v_s) = 800 × 343/318 = 862.9 Hz. 858.3 Hz comes from wrongly using the moving-observer formula.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. Two point charges of 1 µC and 9 µC are 5 cm apart in air. What force acts between them?

  1. 32.4 N
  2. 1.62 N
  3. 129 N
  4. 0.0324 N
Show the answer and solution

Answer: A. 32.4 N

F = kq₁q₂/r² = 8.99×10⁹ × 1×10⁻⁶ × 9×10⁻⁶ / 0.05² = 32.4 N.

10. Sound travels at 343 m/s in air at 20 °C. What is the wavelength of a 1000 Hz tone?

  1. 172 mm
  2. 343 mm
  3. 2.92 m
  4. 300 km
Show the answer and solution

Answer: B. 343 mm

λ = v/f = 343/1000 = 343 mm.

Other topics in the same subjects

Physics: mechanics · General chemistry · Thermodynamics · Engineering materials · Engineering economics · Engineering management · Computer fundamentals and programming · RA 9292 and ethics (electronics) · Fluid mechanics · Strength of materials · RA 7920 and ethics (electrical) · PEC Part 1: general requirements

An independent, free reviewer: not affiliated with the PRC or the Boards. Subject weights and passing rules are from the PRC examination programs and the laws (RA 9292, RA 7920); check the current PRC program before you file. Code questions follow the Philippine Electrical Code 2017 Part 1; check them against your own copy of the Code.