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

Key concepts

Momentum Transfer in Electromagnetic Waves

When electromagnetic waves strike a material, they not only carry energy but also transfer momentum. This might seem surprising because we usually associate momentum with objects that have mass, like balls or cars. However, electromagnetic waves, although massless, carry momentum due to their nature.
When light hits a surface, part of its momentum can be absorbed. This causes a tiny push on the surface. \(P eq 0\) means the wave transfers momentum to the material. This happens because the oscillating electric and magnetic fields in the wave exert forces on the charged particles in the material.

• Momentum transfer is a result of interactions between the wave and the material's charged particles.
• It demonstrates the wave's ability to exert force, influencing the material's atoms.

Energy Transfer in Electromagnetic Waves

Electromagnetic waves are renowned for their ability to carry and transfer energy. When these waves encounter a surface, they deliver energy, which can be absorbed by the material.
Energy is carried in the form of oscillating electric and magnetic fields. The amount of energy transferred depends on the wave's frequency and amplitude. The relationship between momentum and energy implies that if momentum \(P\) is transferred, energy \(E\) is also likely transferred.

• The energy in an electromagnetic wave can cause heating or other reactions in the material.
• Energy transfer is a fundamental aspect of how waves interact with matter.

Oscillating Electric and Magnetic Fields

An electromagnetic wave is like a symphony of oscillating fields. Both electric and magnetic fields oscillate perpendicularly to the direction the wave travels and to each other. This unique configuration is what allows these fields to propagate energy and momentum over vast distances.
The electric field (\(E\)) and magnetic field (\(B\)) change in a synchronized manner, creating a continuous transfer of energy and momentum. The fields are intimately linked, with changes in one inducing changes in the other.

• The oscillation of these fields occurs at specific frequencies, determining the type of electromagnetic wave (e.g., radio, light, X-ray).
• This interplay is key for both the momentum and energy carried by the wave.