Worksheet: Propagating Electric and Magnetic Fields

In this worksheet, we will practice modeling electromagnetic waves as propagating electric and magnetic fields.

Q1:

Electromagnetic waves propagate through water that has a refractive index of 1.33. The electric permittivity of the water is 12×10 C2/N⋅m2. What is the magnetic permeability of the water?

  • A3.7×10 H/m
  • B1.6×10 H/m
  • C5.2×10 H/m
  • D1.6×10 H/m
  • E1.9×10 H/m

Q2:

Which of the following formulas correctly shows the relation between 𝑐, the speed at which electromagnetic waves propagate through a medium; 𝜀, the electric permittivity of the medium; and 𝜇, the magnetic permeability of the medium?

  • A𝑐=𝜇𝜀
  • B𝑐=𝜀𝜇
  • C𝑐=(𝜀𝜇)
  • D𝑐=1(𝜀𝜇)
  • E𝑐=1𝜀𝜇

Q3:

At what speed do electromagnetic waves propagate in a vacuum? Answer to two significant figures.

  • A9.0×10 m/s
  • B9.0×10 m/s
  • C3.0×10 m/s
  • D3.0×10 m/s
  • E3.4×10 m/s

Q4:

Which of the following statements about the energy transferred by the electric and magnetic fields that electromagnetic waves are comprised of is correct?

  • AThe energy transferred by the electric field of an electromagnetic wave is greater than the energy transferred by the magnetic field of the electromagnetic wave.
  • BThe energy transferred by the electric field of an electromagnetic wave is equal to the energy transferred by the magnetic field of the electromagnetic wave.
  • CThe energy transferred by an electromagnetic wave is equal to the difference between the energy transferred by the wave’s electric and magnetic fields.
  • DThe energy transferred by the magnetic field of an electromagnetic wave is greater than the energy transferred by the electric field of the electromagnetic wave.

Q5:

Electromagnetic waves propagate through rubber that has a refractive index of 1.5. The electric permittivity of the rubber is 3.0×10 C2/N⋅m2. What is the magnetic permeability of the rubber?

  • A1.6×10 H/m
  • B1.3×10 H/m
  • C1.7×10 H/m
  • D8.3×10 H/m
  • E3.7×10 H/m

Q6:

Which of the following diagrams correctly shows how the electric field 𝐸, shown in yellow, and the magnetic field 𝐵, shown in green, that an electromagnetic wave is comprised of vary with time 𝑡?

  • A
  • B
  • C
  • D

Q7:

A material has an electric permittivity of 10.4×10 C2/N⋅m2 and a magnetic permeability of 1.78×10 H/m. What is the refractive index of the material?

Q8:

The diagram shows a conducting wire and the magnetic field around it at an instant 𝑡. At the instant 𝑡, the magnetic field around the wire has a nonzero magnitude only as far from the wire as the point that intersects the line 𝐴. The current in the wire is initially zero at an instant 𝑡, which occurs well before 𝑡. The current increases from a value of zero at the instant 𝑡 to a constant nonzero value. The time taken for the current to reach its constant nonzero value is much less than 𝑡𝑡.

Between which of the points that intersect the lines 𝐴, 𝐵, and 𝐶 does the magnetic field strength around the wire not change with time just after the instant 𝑡?

  • A𝐴 and 𝐵
  • B𝐵 and 𝐶
  • CNone of these points
  • D𝐴 and 𝐶

Between which of the points that intersect the lines 𝐴, 𝐵, and 𝐶 is the magnetic field strength constant with the distance from the wire at the instant 𝑡?

  • A𝐵 and 𝐶
  • BNone of these points
  • C𝐴 and 𝐶
  • D𝐴 and 𝐵

Between which of the points that intersect the lines 𝐴, 𝐵, and 𝐶 does the magnetic field strength change with time just after the instant 𝑡?

  • A𝐵 and 𝐶
  • B𝐴 and 𝐶
  • C𝐴 and 𝐵
  • DNone of these points

Between which of the points that intersect the lines 𝐴, 𝐵, and 𝐶 is an electric field present at the instant 𝑡?

  • ANone of these points
  • B𝐴 and 𝐶
  • C𝐴 and 𝐵
  • D𝐵 and 𝐶

Between which of the points that intersect the lines 𝐴, 𝐵, and 𝐶 is an electric field that is changing strength present just after the instant 𝑡?

  • ANone of these points
  • B𝐴 and 𝐵
  • C𝐵 and 𝐶
  • D𝐴 and 𝐶

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