Poynting Vector

Poynting Vector as the name suggests is a quantity that has both magnitude and direction. In the electrical industry, whilst dealing with electromagnetic waves, we often have to come across some tools that can help us analyze these waves. If we think about how electromagnetic waves travel, we realize that we need a term to define the energy flux density of these waves and this is represented by Poynting Vector. Basically, the Poynting vector represents power per unit area. It generally is defined as the cross-product of an electric field and magnetic field, giving us the direction of energy flux which is in the direction of wave propagation. In this article, we will learn about Poynting Vector, its meaning, and its physical Interpretation. We will also discuss the components used in the formula of the Poynting vector. Later we will discuss some advantages and disadvantages of the Poynting vector and how are they put into use. We will conclude the article with some Frequently Asked Questions.

What is Poynting Vector?

Poynting vector was introduced in 1884 by English physicist John Henry Poynting, thereby naming it after his name . Poynting vector is a tool used for studying energy flow in electromagnetic waves. In layman’s language, it is used to tell how much energy is being carried by an electromagnetic wave in a unit area. The formal definition is given below

Poynting vector represents the power per unit area transported by an electromagnetic wave. It is denoted by letter S.

Thereby this vector helps us understand how the transfer of energy works, and how can we determine the direction where energy is going to flow. For example, it helps us understand how waves being emitted from an antenna carry energy.

Physical Interpretation of Poynting Vector

In order to understand what the Poynting vector physically signifies, we need to understand the definition of the Poynting vector and understand the physics behind it.

In physics, the Poynting vector gives us the directional energy flux or power flow of an electromagnetic field. we can understand energy flux as the energy transfer per unit area, per unit time. The cross product in the Poynting vector signifies the direction in which energy is transported. The magnitude of the Poynting vector denotes the power per unit area i.e. the power density of the electromagnetic wave.

Hence we can say that the vector provides us with direction and intensity of energy flow within an electromagnetic field.

Poynting Theorem

The physical interpretation of Poynting vector can be understood by Poynting theorem which states that

Poynting’s theorem states that the rate of energy transfer per unit volume from a region of space equals the rate of work done on the charge distribution in the region, plus the energy flux leaving that region.

Formula of Poynting

Formally, Poynting vector is the cross product of electric field(E) and magnetic field(B), respectively. Note that the order in which these terms are written is very necessary.

Electromagnetic Wave

Poynting vector= cross product of electric field and magnetic field

S=E×B/ μ

S is Poynting Vector

E is Electric Field

B is Magnetic Field

Here it is important to note that the Poynting vector represents the direction and magnitude of energy flow. The electric field is the field that causes a charged particle to experience the force in an electromagnetic field. The magnetic field is responsible for all the the magnetic properties of the electromagnetic wave.

To calculate the magnitude of Poynting vector ,we can further represent cross product in terms of sin(θ) as

|S| = 1/μ₀(|E| * |B| * sin(θ))

|E| is magnitude of the electric field

|B| is magnitude of the magnetic field

θ is angle between the two fields.

μ₀= vacuum permeability = 1.257 x 10^-6 henry/ meter

Advantages of Poynting Vector

Poynting vector ahs various advantages like:

• It helps in calculation of direction of flow on energy. It helps in studying how EM waves interact and propagate with surroundings.
• The magnitude of Poynting vector gives us the power density of the electromagnetic field at a specific point. This helps to study field intensity at different points in the surroundings.
• Since Poynting vector is consistent with conservation of energy principle, it can be used to verify that the total power entering a given region is equal to the total power leaving that region at different places.
• It is easy to calculate since it only involves solving a cross product of two fields.

Disadvantages of Poynting Vector

There are some limitations of Poynting vector like :

• With modifications in surroundings like surroundings which involve time dependent electric and magnetic field, it becomes very difficult to measure Poynting vector as it becomes complex. Thereby it is not always viable in some practical situations.
• Poynting vector is based on some assumptions of ideality like presence of linear, isotropic, and homogeneous media. on contrast to this the real-world doesn’t fulfil these ideal conditions due to non-uniform environments thereby dropping the accuracy of Poynting vector.
• The applications of Poynting vector are limited to a particular kind of waves i.e Electromagnetic waves. This can’t be applied to other waves without making necessary modifications making its use limited to certain waves only.

Vector Applications of Poynting Vector

Poynting vector is applicable to large number of places like:

• It is used in the study of electromagnetic wave propagation. As the formula helps to analyse the direction of wave propagation, engineers use this to strategize and study optimal methods of wave propagation in wireless systems.
• It is used for designing antennas. Since we know antennas are used for communication and must have a large range of coverage with minimal energy loss, Poynting vector helps to analyse the antenna design for efficient energy transfer.
• Astrophysics makes use of Poynting vector while analysing energy transmission of celestial objects like stars, moon. This is done to get better perspective of universe. It is also used to assess the power received from sun.
• It is also used to study various other topics in physics like radiation pressure.

Solved Examples

1. A radio transmitter emits an electromagnetic wave with an electric field magnitude of 3 V/m and generates a magnetic field magnitude of 2 μT. Calculate the magnitude of the Poynting Vector at a point where the angle between E and B is 30 degrees.

Using the formula |S| = |E| * |B| * sin(θ), we can calculate:

|S| = 3 V/m * 2 μT * sin(30°) = 3× 10^-6W/m²

So, at this point, the magnitude of the Poynting Vector is 3 ×10^-6W/m²

2. A horn antenna radiates an electromagnetic wave with an electric field magnitude of 10 V/m and a magnetic field magnitude of 5 μT. Calculate the power radiated per unit area.

Using the Poynting Vector formula, we can calculate the power per unit area:

Power = |S| = |E| * |B| = 10 V/m * 5 μT = 50 ×10^-6W/m²

So, the power radiated per unit area is 50 x 10−6
W/m².

Conclusion

As we discussed about the Poynting vector in this article, we realized how significant it is when talking about electromagnetic waves. We have seen the representation of this vector and discussed how we can represent it in terms of electric and magnetic field. In nutshell, we read how Poynting vector is used for showing the magnitude and direction of energy associated with electromagnetic waves. This concept is to put to use in various applications like discussing about radio waves, study the power flow in space and many more. Readers can further enhance their knowledge of subject by referring to the frequency asked questions.

FAQs on Poynting Vector

1. What are the units of Poynting vector?

As Poynting vector represents power per unit area, it has the units as watts per square meter (W/m²)

2. What is radiation Pressure?

It can be defined as the mechanical pressure that is applied on any surface mainly because of momentum exchange between the electromagnetic field and the object. Engineers use the Poynting vector to calculate the intensity of the incident radiation for calculating this pressure.

3. Is Poynting vector applicable to any wave with no restrictions?

Poynting vector is mainly used for plane waves in free space like electromagnetic waves. In is not made for other kinds of waves but can be modified based on requirements.