Problem 2 - University Physics with Modern Physics

Question

Which of the following statements concerning electromagnetic waves are incorrect? (Select all that apply.) a) Electromagnetic waves in vacuum travel at the speed of light. b) The magnitudes of the electric field and the magnetic field are equal. c) Only the electric field vector is perpendicular to the direction of the wave's propagation. d) Both the electric field vector and the magnetic field vector are perpendicular to the direction of propagation. e) An electromagnetic wave carries energy only when \(E=B\).

Step-by-Step Solution

Answer

a) Electromagnetic waves in a vacuum travel at the speed of light. b) The magnitudes of the electric field and magnetic field are equal. c) Only the electric field vector is perpendicular to the direction of the wave's propagation. d) Both the electric field vector and the magnetic field vector are perpendicular to the direction of propagation. e) An electromagnetic wave carries energy only when the magnitudes E and B are equal. Answer: The incorrect statements concerning electromagnetic waves are (b), (c), and (e).

Step 1: Understand properties of electromagnetic waves

Electromagnetic waves are disturbances created in both the electric and magnetic fields that propagate through space. Some key properties to remember are: 1. Electromagnetic waves in a vacuum travel at the speed of light (\(c\)). 2. The electric field vector (\(\vec{E}\)) and the magnetic field vector (\(\vec{B}\)) are always perpendicular to each other and to the direction of propagation. Now let's analyze each statement to identify the incorrect ones.

Step 2: Analyze statement (a)

Statement (a) says that electromagnetic waves in vacuum travel at the speed of light. This statement is correct, as it matches the first key property of electromagnetic waves mentioned above.

Step 3: Analyze statement (b)

Statement (b) claims that the magnitudes of the electric field and magnetic field are equal. This statement is not necessarily true, as the magnitudes of the electric field and magnetic field can vary depending on the medium and polarization. So, statement (b) is incorrect.

Step 4: Analyze statement (c)

Statement (c) says that only the electric field vector is perpendicular to the direction of the wave's propagation. This statement is incorrect because, as mentioned in step 1, both the electric field vector and the magnetic field vector are perpendicular to the direction of propagation.

Step 5: Analyze statement (d)

Statement (d) states that both the electric field vector and the magnetic field vector are perpendicular to the direction of propagation. This statement is correct and matches the second key property mentioned in step 1.

Step 6: Analyze statement (e)

Statement (e) claims that an electromagnetic wave carries energy only when the magnitudes \(E\) and \(B\) are equal. This statement is incorrect because the energy carried by an electromagnetic wave is the product of the magnitudes of electric field (\(E\)) and magnetic field (\(B\sin\theta\)), where \(\theta\) is the angle between the electric field vector and magnetic field vector. Such a product doesn't require equal magnitudes of \(E\) and \(B\).

Step 7: Identify the incorrect statements

Based on the above discussion, the incorrect statements concerning electromagnetic waves are (b), (c), and (e).