Worksheet: Electric and Magnetic Fields in Electromagnetic Waves

In this worksheet, we will practice modeling the relationship between the magnitude changes with time of magnetic and electric fields in electromagnetic waves.

Q1:

A radio transmitter broadcasts plane electromagnetic waves whose electric field amplitude at a particular location is 1 . 5 5 0 × 1 0 3 V/m. What is the amplitude of the electromagnetic wave’s magnetic field at that location?

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

Q2:

A plane electromagnetic wave travels northward. At one instant, its electric field has a magnitude of 6.0 V/m and points eastward. What is the magnitude of the magnetic field at this instant?

  • A 2 . 7 × 1 0 8 T
  • B 2 . 3 × 1 0 8 T
  • C 3 . 0 × 1 0 8 T
  • D 2 . 0 × 1 0 8 T
  • E 3 . 3 × 1 0 8 T

Q3:

A certain 60.0-Hz ac power line radiates an electromagnetic wave having a maximum electric field strength of 13.0 kV/m.

What is the wavelength of this very-low-frequency electromagnetic wave?

  • A 4 . 6 3 × 1 0 6 m
  • B 4 . 5 0 × 1 0 6 m
  • C 4 . 8 0 × 1 0 6 m
  • D 5 . 0 0 × 1 0 6 m
  • E 4 . 8 8 × 1 0 6 m

What is the magnitude of the strongest magnetic field present in this wave?

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

Q4:

A radio station broadcasts at a frequency of 760 kHz. At a receiver some distance from the antenna, the maximum magnetic field of the electromagnetic wave detected is 2 . 1 5 × 1 0 1 1 T.

What is the maximum electric field amplitude?

  • A 6 3 6 × 1 0 3 V/m
  • B 6 2 8 × 1 0 3 V/m
  • C 6 5 8 × 1 0 3 V/m
  • D 6 4 5 × 1 0 3 V/m
  • E 6 7 0 × 1 0 3 V/m

What is the wavelength of the electromagnetic wave?

Q5:

During a heartbeat, a heart produces a maximum potential of 4.00 mV across a 0.300-m distance. The changing potential generates a 1.00-Hz electromagnetic wave.

What is the maximum electric field strength produced during the heartbeat?

  • A 1 . 3 9 × 1 0 V/m
  • B 1 . 2 5 × 1 0 V/m
  • C 1 . 4 6 × 1 0 V/m
  • D 1 . 3 3 × 1 0 V/m
  • E 1 . 5 3 × 1 0 V/m

What is the maximum magnetic field strength produced during the heartbeat?

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

What is the wavelength of the electromagnetic wave produced by the heartbeat?

  • A 3 . 1 3 × 1 0 m
  • B 2 . 9 0 × 1 0 m
  • C 3 . 0 0 × 1 0 m
  • D 2 . 9 5 × 1 0 m
  • E 3 . 0 8 × 1 0 m

Q6:

In a region of space, the electric field is pointed along the 𝑥 -axis, but its magnitude changes as described by

where 𝑡 is in nanoseconds and 𝑥 is in cm. Find the displacement current through a circle of radius 3.000 cm in the 𝑥 = 0 plane at 𝑡 = 0 .

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

Q7:

The strengths of an electric and a magnetic field vary sinusoidally in time with a frequency 𝑓 = 0 . 6 5 G H z . Both the field’s strengths are initially zero at the instant 𝑡 0 s, after which the strength of the electric field 𝐸 = 𝐸 ( 2 𝜋 𝑓 𝑡 ) 0 s i n and the strength of the magnetic field 𝐵 = 𝐵 ( 2 𝜋 𝑓 𝑡 ) 0 s i n .

What is the first value of 𝑡 > 𝑡 0 for which the strengths of both the electric and the magnetic fields are zero?

What is the first value of 𝑡 > 𝑡 0 when the strengths of both the electric and the magnetic fields are at their greatest negative value?

How much time is needed for both the electric and the magnetic fields to complete one cycle?

Q8:

What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of 2 . 8 0 × 1 0 4 T?

  • A 6 3 . 0 × 1 0 3 V/m
  • B 4 2 . 5 × 1 0 3 V/m
  • C 5 5 . 0 × 1 0 3 V/m
  • D 8 4 . 0 × 1 0 3 V/m
  • E 2 1 . 5 × 1 0 3 V/m

Q9:

A radio station broadcasts radio waves at a frequency of 100.6 MHz. The radio waves move through the air at effectively the speed of light in a vacuum. What is the wavelength of the radio waves?

Q10:

The magnetic field of a plane electromagnetic wave moving along the 𝑧 -axis is given by 𝐵 = 𝐵 ( 𝑘 𝑧 + 𝜔 𝑡 ) 𝑗 c o s , where 𝐵 = 3 . 0 0 × 1 0 T and 𝑘 = 2 . 2 4 × 1 0 m−1.

What is the frequency of the wave?

What is the wavelength of the wave?

What is the average Poynting vector of the wave?

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

Q11:

A microwave oven uses electromagnetic waves of frequency 5 . 3 7 × 1 0 9 Hz to heat food. The waves reflect from the inside walls of the oven to produce an interference pattern of standing waves. The antinodes of these standing waves are points that have radiation of the highest intensity and can leave observable pit marks when cooking some foods. For a particular food, these pit marks are measured to be 4.0 cm apart. Calculate the speed of the electromagnetic waves indicated by this pit mark separation.

  • A 1 . 3 × 1 0 8 m/s
  • B 4 . 2 × 1 0 8 m/s
  • C 6 . 4 × 1 0 8 m/s
  • D 2 . 1 × 1 0 8 m/s
  • E 8 . 3 × 1 0 8 m/s

Q12:

The most efficient length for a vertically aligned broadcast antenna, which has one end located at ground level, emitting electromagnetic waves of wavelength 𝜆 is 𝜆 4 . A radio station has a vertically aligned antenna with a length of 43.0 m. At what frequency does the antenna emit most efficiently?

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