Question

For an electromagnetic wave, the phase difference between vectors \(\mathrm{E}^{-}\) and \(\mathrm{B}^{-}\) (far away from the source) (A) 0 (B) \([\pi / 2]\) (C) \(\pi\) (D) \([3 \pi / 2]\)

Short answer

For an electromagnetic wave far away from the source, the electric field vector \(\mathrm{E}^{-}\) and the magnetic field vector \(\mathrm{B}^{-}\) are in phase with each other, meaning they reach their maximum and minimum values simultaneously. Therefore, the phase difference between these vectors is 0. So the correct answer is (A) 0.

Step-by-step solution

Recall the properties of electromagnetic waves

Electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and the direction of wave propagation. They travel at the speed of light, and their electric and magnetic fields are related by the equation: \[c = \frac{E}{B}\], where \(c\) is the speed of light, and \(E\) and \(B\) represent the magnitudes of the electric field and magnetic field, respectively.

Identify the phase difference between the electric and magnetic fields

In electromagnetic waves, the electric and magnetic fields oscillate sinusoidally and they are in phase with each other. This means that the electric and magnetic fields both reach their maximum and minimum values simultaneously. Therefore, the phase difference between the electric field vector \(\mathrm{E}^{-}\) and the magnetic field vector \(\mathrm{B}^{-}\) is 0.

Choose the correct answer

From the given options, the correct answer that represents the phase difference between the electric field vector \(\mathrm{E}^{-}\) and the magnetic field vector \(\mathrm{B}^{-}\) is: (A) 0

Key concepts

Phase Difference

In the context of electromagnetic waves, phase difference refers to the difference in phase angle between two sinusoidally varying quantities. For electromagnetic waves, the key quantities of interest are the electric ( E ) and magnetic ( B ) fields. Phase plays a significant role in understanding how these fields interact and propagate through space.

In electromagnetic waves, the electric and magnetic fields are said to be "in phase" when they both reach their maximum and minimum values at the same time. This means there is no phase difference between them, translating into a phase difference of zero. In phase terms, if both fields start and end at the same position on a wave cycle simultaneously, they are said to be synchronized.

Having a phase difference of zero means that these fields oscillate together perfectly, reinforcing each other as they propagate. This is crucial for the consistent transmission of energy across space, as any phase difference could lead to disruptions in how the wave carries energy. Understanding this helps to elucidate why electromagnetic waves can travel vast distances effectively.

Electric Field (E)

The electric field ( E ) is a fundamental characteristic of an electromagnetic wave. It represents the force that would be experienced by a charge placed in the field, due to the wave's electric component. The electric field is a vector field, meaning it has both magnitude and direction.

In an electromagnetic wave, the electric field oscillates perpendicularly to the direction of wave propagation. This oscillation helps to perpetuate the wave's continuous transmission. The magnitude of the electric field is directly proportional to the strength of the wave. A stronger wave will typically have a more substantial electric component.

Moreover, electric fields can exist independently; however, within electromagnetic waves, they interact harmoniously with magnetic fields. This interaction is guided by Maxwell's equations, which describe how changing electric fields can induce magnetic fields, and vice versa. Understanding electric fields is integral to comprehending a wide range of phenomena, from radio waves to visible light.

Magnetic Field (B)

The magnetic field ( B ) is another essential component of electromagnetic waves. Like the electric field, the magnetic field is also a vector field, adding another layer of complexity to wave behavior.

In electromagnetic waves, the magnetic field oscillates perpendicular to both the electric field and the direction of wave propagation. The relationship between the magnetic and electric fields is vital because they influence each other's behavior and ensure the wave's stability. This intricate dance between the fields is facilitated by the fact that they are in phase, ensuring they reinforce each other for consistent wave propagation.

Magnetic fields, when part of electromagnetic waves, maintain energy conservation through their precise phase interactions. The fields are intertwined in such a way that they constantly support each other, allowing the wave to travel at the speed of light. As such, magnetic fields are indispensable in understanding how electromagnetic waves move and interact with matter.