Poynting Vector - Finding stored energy per unit length of a solenoid


by physicsoxford
Tags: energy, length, poynting, solenoid, stored, unit, vector
physicsoxford
physicsoxford is offline
#1
Feb28-12, 12:22 PM
P: 4
1. The problem statement, all variables and given/known data

long solenoid of n turns per unit length is wound upon a cylindrical core of radius a
and relative permeability. The current I through the solenoid is increasing with time t at a
constant rate. Obtain expression for the rate of increase of stored energy per unit length in the core
of the solenoid
(a) from the inductance per unit length of the solenoid, and dI=dt.
(b) from the energy associated with the fields internal to the solenoid core.
(c) by integration of the Poynting vector over an appropriate surface.

2. Relevant equations

None are given but I believe this is what should be considered:

-∂/∂t ∫[ εE2/2 + B2/2μ ] dv = ∫ Jf dot E dv + ∫ E cross H da

Ampere's Law

E cross H = S

3. The attempt at a solution

Using Ampere's Law: B=μnI

L = flux/I
L = μn2lA Where l is some length and A is a surface


Part A)

∅ = L dI/dt

∅ = μn2lA dI/dt

U = Q∅/2

U/dt = μn2lA (dI/dt) (Q/dt) (1/2)

U/dt = μn2lA (dI/dt) I (1/2)

This just does not seem right to me??

Part B)

U = ∫B2/2μ dv

U = ∫(μnI)2/2μ dv

U = μn2lAI (1/2)

U/dt = μn2lA (dI/dt) I (1/2)

Part C)

U = ∫ S dv

where S = E cross H, assuming ∫ Jf dot E dv = 0

This is where I am confused. Is there an electric field in the solenoid? If so then did I not do the other parts correctly? What am I missing here...
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
rude man
rude man is offline
#2
Mar3-12, 02:57 AM
HW Helper
Thanks
PF Gold
rude man's Avatar
P: 4,408
Not that complicated. Given inductance L, what is the formula for stored energy?

Then, calculate L per unit length.


Register to reply

Related Discussions
electrical energy stored in solenoid Classical Physics 3
Energy stored and # turns in an MRI machine (solenoid) Introductory Physics Homework 6
Energy Stored in Magnetic Field of Solenoid Introductory Physics Homework 2
Finding and using the Poynting vector Introductory Physics Homework 0
Relating time averaged energy density to the Poynting vector per unit solid angle Advanced Physics Homework 3