Worksheet: Energy, Power, and Intensity of Electromagnetic Waves

In this worksheet, we will practice calculating the energy, power, and intensity of electromagnetic waves and the magnitude of the Poynting vector.

Q1:

An outdoor WiFi unit for a picnic area has a 100-mW output and a range of about 30 m. What output power would reduce its range to 12 m for use with the same devices as before? Assume there are no obstacles in the way and that microwaves into the ground are simply absorbed.

Q2:

Two lightbulbs have electrical power inputs of 100 W and 75 W respectively. At what distance is the intensity of light produced by the 100 W lightbulb equal to the intensity of light 10.0 m away from the 75 W lightbulb? Assume that both lightbulbs have the same efficiency.

Q3:

What is the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m?

Q4:

A 150-W lightbulb emits 5.00% of its energy as electromagnetic radiation. What is the magnitude of the average Poynting vector 10.0 m from the bulb?

  • A 5 . 9 7 × 1 0 W/m2
  • B 6 . 1 1 × 1 0 W/m2
  • C 5 . 5 9 × 1 0 W/m2
  • D 5 . 8 5 × 1 0 W/m2
  • E 5 . 7 4 × 1 0 W/m2

Q5:

At the top of Earth’s atmosphere, the time-averaged Poynting vector associated with sunlight has a magnitude of 1.40 kW/m2.

What is the maximum value of the electric field magnitude for a wave of this intensity?

What is the maximum value of the magnetic field magnitude for a wave of this intensity?

  • A 3 . 5 1 × 1 0 T
  • B 3 . 6 0 × 1 0 T
  • C 3 . 7 2 × 1 0 T
  • D 3 . 4 2 × 1 0 T
  • E 3 . 3 6 × 1 0 T

What is the total power radiated by the sun? Assume that the Earth is 1.50×10 m from the Sun and that sunlight is composed of electromagnetic plane waves.

  • A 4 . 7 7 × 1 0 W
  • B 3 . 0 3 × 1 0 W
  • C 3 . 9 6 × 1 0 W
  • D 5 . 5 9 × 1 0 W
  • E 2 . 1 6 × 1 0 W

Q6:

The specific heat capacity of spaghetti is 3.76×10/JkgC. 0.400 kg of spaghetti occupies a circular area 20.0 cm in diameter inside a microwave oven. On its highest power setting, the oven increases the temperature of the spaghetti by 45.0C in 120 s.

What was the rate of energy absorption by the spaghetti, assuming that the spaghetti was perfectly absorbing?

Find the average intensity of the microwaves.

  • A 2 . 3 3 × 1 0 W/m2
  • B 1 . 5 6 × 1 0 W/m2
  • C 2 . 6 3 × 1 0 W/m2
  • D 2 . 0 7 × 1 0 W/m2
  • E 1 . 8 0 × 1 0 W/m2

What is the peak electric field strength of the microwave?

  • A 3 . 8 9 × 1 0 V/m
  • B 4 . 0 3 × 1 0 V/m
  • C 3 . 7 7 × 1 0 V/m
  • D 3 . 6 8 × 1 0 V/m
  • E 4 . 1 1 × 1 0 V/m

What is the peak magnetic field strength of the microwave?

  • A 1 . 2 3 × 1 0 T
  • B 1 . 4 0 × 1 0 T
  • C 1 . 2 9 × 1 0 T
  • D 1 . 3 5 × 1 0 T
  • E 1 . 4 4 × 1 0 T

Q7:

An AM radio transmitter broadcasts 50.0 kW of power uniformly in all directions. Assume that radio waves that strike the ground are completely absorbed and that no absorption of radio waves occurs except at the ground, so that half of the emitted power will be spread over a hemispherical area. Radio waves from the transmitter reach a receiver that is located 30.0 km away from the transmitter.

What is the intensity of the radio waves at the receiver’s location?

  • A 2 . 7 4 × 1 0 W/m2
  • B 6 . 6 7 × 1 0 W/m2
  • C 3 . 5 9 × 1 0 W/m2
  • D 4 . 4 2 × 1 0 W/m2
  • E 5 . 3 3 × 1 0 W/m2

What is the maximum electric field strength of the radio waves at the receiver’s location?

  • A 5 . 5 2 × 1 0 W/m2
  • B 5 . 7 7 × 1 0 W/m2
  • C 5 . 6 6 × 1 0 W/m2
  • D 6 . 0 8 × 1 0 W/m2
  • E 5 . 9 0 × 1 0 W/m2

Q8:

The filament in a clear incandescent light bulb radiates 4.00 W of visible light. The glass part of the bulb can be modeled as a sphere of radius 1.80 cm and the filament can be treated as a point at the center of the sphere. Find the intensity of the visible light at the surface of the bulb.

Q9:

To increase the intensity of a wave by a factor of 20, by what factor should the amplitude be increased?

Q10:

Energy from the Sun arrives at the closest planet to it, Mercury, with an average intensity of 10.4×10 W/m2. How long does it take for 1.32×10 J to arrive at an area of 1.00 m2 on Mercury?

Q11:

A photovoltaic array of solar cells is 8.00% efficient in gathering solar energy and converting it to electricity. Assume a value of 75.0 W/m2 for the average intensity of sunlight.

What area should the array have to gather energy at the rate of 250 W?

What is the maximum cost of the array if it must pay for itself in two years of operation, averaging 12.00 hours of use per day? Assume that the array earns money at the rate of 10 cents per kilowatt-hour.

Q12:

A laser beam is used to burn away cancerous tissue. When 93.0% of the energy in the beam is absorbed, the beam concentrates 0.550 kJ of energy into a circular spot that is 1.75 mm in diameter in a time of 3.50 s. What is the intensity of the beam?

  • A 2 . 2 1 × 1 0 W/m2
  • B 7 . 0 2 × 1 0 W/m2
  • C 6 . 5 3 × 1 0 W/m2
  • D 6 . 1 5 × 1 0 W/m2
  • E 5 . 5 2 × 1 0 W/m2

Q13:

A radio station broadcasts its radio waves with a power of 80 kW. What would the intensity of this signal be if it was received on a planet orbiting Proxima Centauri, the closest star to our Sun, 4.243 ly away from the point the radiation was emitted from? Answer to one significant figure.

  • A 7 × 1 0 W/m2
  • B 5 × 1 0 W/m2
  • C 3 × 1 0 W/m2
  • D 4 × 1 0 W/m2
  • E 2 × 1 0 W/m2

Q14:

The Andromeda galaxy is the closest large galaxy to the Milky Way and is visible to the naked eye. Find the brightness of the Andromeda galaxy relative to the Sun. Model the Andromeda galaxy as having a luminosity 1.00×10 times that of the Sun and being at a 0.622 Mpc distance from an observer.

  • A 3 . 1 1 × 1 0 W/m2
  • B 6 . 2 2 × 1 0 W/m2
  • C 1 . 8 7 × 1 0 W/m2
  • D 2 . 1 6 × 1 0 W/m2
  • E 0 . 3 7 8 × 1 0 W/m2

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