Question

A plane electromagnetic wave is incident on a mater1al surface. The wave delivers momentum \(P\) and energy \(E\) (A) \(\mathrm{P}=0, \mathrm{E} \neq 0\) (B) \(\mathrm{P} \neq 0, \mathrm{E}=0\) (C) \(P \neq 0, E \neq 0\) (D) \(P=0, E=0\)

Short answer

The correct answer is (C) \(P \neq 0, E \neq 0\), as an electromagnetic wave carries both momentum and energy away from its source. When the wave interacts with a material, it can deliver both momentum and energy to the material.

Step-by-step solution

Understand the properties of electromagnetic waves

An electromagnetic wave consists of oscillating electric and magnetic fields, which create a flow of energy and momentum as they propagate. An electromagnetic wave carries both energy and momentum away from its source. When the wave interacts with a material, momentum and energy can be transferred from the wave to the material. In this question, we will check which options satisfy these conditions.

Analyze option (A)

Option (A) states that the wave delivers no momentum (P=0) but delivers energy (E≠0) to the material. We know that an electromagnetic wave carries both momentum and energy as it propagates. If an electromagnetic wave delivers energy to the material, it is also delivering momentum since both are tied together in an electromagnetic wave.

Analyze option (B)

Option (B) states that the wave delivers momentum (P≠0) but delivers no energy (E=0) to the material. We know that an electromagnetic wave carries both momentum and energy as it propagates. If an electromagnetic wave delivers momentum to the material, it is also delivering energy since they are interconnected. It is not possible for the wave to deliver momentum without delivering energy.

Analyze option (C)

Option (C) states that the wave delivers momentum (P≠0) and energy (E≠0) to the material. Since electromagnetic waves carry both momentum and energy as they propagate, we know that an electromagnetic wave can indeed transfer both of these quantities to the material. This option is consistent with our understanding of electromagnetic waves.

Analyze option (D)

Option (D) states that the wave delivers no momentum (P=0) and no energy (E=0) to the material. If an electromagnetic wave does not interact with the material at all, it is possible for it to not deliver any momentum or energy. However, that is not the case here, as we are given that the wave is incident on the material surface. Since the wave is interacting with the material, it should transfer some momentum and energy. Based on the analysis of each option, we can conclude that the answer is: (C) P≠0, E≠0