Poynting's theorem in a solenoid

In summary, the conversation discusses the verification of Poynting's theorem for a cylindrical solenoid with a current flowing through it. The solution involves solving for the current using Ldi/dt=Ri and verifying conservation of energy through calculations. The conversation also mentions difficulties with expressing current density and the potential for a large amount of calculations.
  • #1
matnatale
1
0

Homework Statement


Consider a cylindrical solenoid(of radius a,and length h>>a,having n turns of wire for unity of lenght),The solenoid is connected to a resistance R and,at instant t=0 a current i(0)=i0 is flowing in the wire.Prove that poynting's theorem is verified for t>0[/B]

Homework Equations

[PLAIN]https://wikimedia.org/api/rest_v1/media/math/render/svg/e6fe1dabe8c9699364d0e983f92139c7a6d4deeb[/B]

The Attempt at a Solution


I assumed the current i(t) could be obtained solving Ldi/dt=Ri,where L is the inductance I previously computed.I tried to verify the conservation of energy applying the theorem in its global form on the volume of the solenoid,but,on one side,i don't know how to express current density J for the solenoid,on the other i realized it would lead me to a massive amount of calculations,Maybe there's some other way I didn't take into account?Sorry for my English.[/B]
 
Last edited by a moderator:
Physics news on Phys.org

Related to Poynting's theorem in a solenoid

1. What is Poynting's theorem in a solenoid?

Poynting's theorem in a solenoid is a mathematical equation that describes the relationship between electric and magnetic fields in a solenoid, a cylindrical coil of wire. It states that the energy flow per unit area, known as the Poynting vector, is equal to the cross product of the electric and magnetic fields.

2. How is Poynting's theorem applied in a solenoid?

In a solenoid, Poynting's theorem is used to calculate the amount of energy that is being transferred through the electromagnetic fields. This energy transfer is important in understanding the behavior and functioning of solenoids in various applications, such as in motors and generators.

3. What is the significance of Poynting's theorem in a solenoid?

Poynting's theorem is significant as it allows us to understand the flow of energy in electromagnetic fields, which is crucial in many practical applications. It also helps in predicting the behavior and performance of solenoids in different situations.

4. How does Poynting's theorem relate to conservation of energy?

Poynting's theorem is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. In a solenoid, the energy flow calculated using Poynting's theorem is equal to the energy input to the system, thus satisfying the law of conservation of energy.

5. Are there any limitations to Poynting's theorem in a solenoid?

One limitation of Poynting's theorem in a solenoid is that it assumes the fields are static and do not change over time. In reality, most solenoids have changing fields, which can affect the accuracy of the calculations. Additionally, the theorem does not take into account other factors such as resistance and losses in the solenoid, which may also impact the energy transfer.

Similar threads

Poynting theorem and electromagnetic density
    • Introductory Physics Homework Help
Replies
7
Views
798
Current in circular wire surrounding infinite solenoid in a circuit
    • Introductory Physics Homework Help
Replies
7
Views
180
Understanding self-inductance in a solenoid.
    • Introductory Physics Homework Help
Replies
3
Views
197
Current through ring in solenoid-ring system
    • Introductory Physics Homework Help
Replies
1
Views
739
Ratio of Inductance between 2 Solenoids?
    • Introductory Physics Homework Help
Replies
3
Views
3K
EMF induced in a coil encircling an ideal solenoid
    • Introductory Physics Homework Help
Replies
2
Views
1K
Parallel Axis Theorem Experiment
    • Introductory Physics Homework Help
Replies
1
Views
3K
Electric Field from Long Hollow Cylinder
    • Introductory Physics Homework Help
Replies
3
Views
3K
Find an expression for the COF
    • Introductory Physics Homework Help
Replies
5
Views
1K
Power Output of Radiation from a Solenoid with Linearly Decreasing Current
    • Introductory Physics Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top