Calculating Poynting Vector in Long Resistive Rod

In summary, the Poynting Vector in a long resistive rod is a mathematical concept that describes the flow of electromagnetic energy. It can be calculated using the formula S = (1/μ)E x B and is affected by factors such as the strength of the fields, material conductivity, and angle between the fields. The Poynting Vector may vary along the length of the rod due to reflections or interference. Understanding and calculating the Poynting Vector is important in applications such as power transmission and device efficiency.
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Homework Statement



Consider a long resistive rod, exhibiting resistance R, of length l and radius r. Calculate the magnitude and direction of the Poynting vector (neglecting edge effects) and relate the rate of energy transfer between the rod and its exterior to the total power dissipated in the rod.


Homework Equations





The Attempt at a Solution



Not sure how to even go about starting this?! Any help please?

I know that N = 1/mu o E x B, but here we aren't given an E or B field?! What to do ?

Thanks!
 
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1. What is the Poynting Vector in a long resistive rod?

The Poynting Vector in a long resistive rod is a mathematical concept used to describe the flow of electromagnetic energy in a long conductive material. It is a vector quantity and represents the direction and magnitude of the energy flow.

2. How is the Poynting Vector calculated in a long resistive rod?

The Poynting Vector in a long resistive rod can be calculated using the formula S = (1/μ)E x B, where S is the Poynting Vector, E is the electric field, B is the magnetic field, and μ is the permeability of the material. This formula takes into account the energy flow in both the electric and magnetic fields.

3. What factors affect the magnitude of the Poynting Vector in a long resistive rod?

The magnitude of the Poynting Vector in a long resistive rod is affected by the strength of the electric and magnetic fields, the conductivity and resistivity of the material, and the permeability of the material. The angle between the electric and magnetic fields also plays a role in determining the magnitude of the Poynting Vector.

4. How does the Poynting Vector change along the length of a long resistive rod?

The Poynting Vector may change along the length of a long resistive rod depending on the factors mentioned above. In general, it decreases as the distance from the source of energy increases. However, in some cases, it may also increase due to reflections or interference in the electromagnetic waves.

5. What is the significance of calculating the Poynting Vector in a long resistive rod?

Calculating the Poynting Vector in a long resistive rod is important in understanding the flow of electromagnetic energy in conductive materials. It is used in various applications such as power transmission, electromagnetic shielding, and antenna design. It also helps in analyzing the efficiency and performance of electric and electronic devices.

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