PHYS208 PHYS208 4/22 Class

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Magnetic Energy

Inductance of a length of Long Solenoid

Inductance of a long solenoid

This is the inductance per length l of a long solenoid having a cross-sectional area A. In class, I demonstrated this result by evaluating the flux linkage per unit current of N = nl turns of the solenoid.

Energy Stored in an Inductor

Energy stored in an inductor

Concept Check -- Second Configuration

Magnetic Energy Density (compared to Electric Energy Density)

Parallel-Plate Capacitor   Long Solenoid
Charged capacitor   Energized inductor
     
Uniform electric field

Plate area A,
plate separation d

  Uniform magnetic field

Turn density n,
cross-sectional area A;
Consider length l.
 

Electric Energy / Volume   Magnetic Energy / Volume
 
Energy density inside capacitor
 
   
Energy density inside solenoid
 
Energy/Volume in Capacitor   Energy/Volume in Solenoid
 
Energy density inside capacitor
 
   
Energy density inside solenoid
 
Capacitance of this Geometry   Inductance of this Geometry
 
Energy density inside capacitor
 
Energy density inside capacitor
 
   
Energy density inside solenoid
 
Energy density inside solenoid
 
Electric Energy Density   Magnetic Energy Density
 
Energy density inside capacitor
 
   
Energy density inside solenoid
 

Although the resulting expressions for the energy density associated with fields has been worked for specific ideal cases involving uniform fields, the formulas for energy density are general results! There is energy associated point-by-point with both electric and magnetic fields.

When we studied the electric energy density earlier in the course, we used it as an alternative way of evaluating capacitance. Similarly we will be using the magnetic energy density integrated over the volume of an inductor to evaluate its inductance. This is especially useful when the flux linkage is difficult to identify, as in the case of the contribution to inductance arising from the field inside the wires of the inductor...


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Last updated April 22, 1998.
Copyright George Watson, Univ. of Delaware, 1997.