PHYS208 4/22 Class

Magnetic Energy

Inductance of a length of 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

Concept Check -- Second Configuration

Magnetic Energy Density (compared to Electric Energy Density)

Parallel-Plate Capacitor		Long Solenoid
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/Volume in Capacitor		Energy/Volume in Solenoid
Capacitance of this Geometry		Inductance of this Geometry
Electric Energy Density		Magnetic Energy Density

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...

"http://www.physics.udel.edu/~watson/phys208/clas0422.html"
Last updated April 22, 1998.
Copyright George Watson, Univ. of Delaware, 1997.