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Energy stored in a toroid 
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#1
Mar306, 01:23 AM

P: 777

Calculate the energy stored in a toroidal coil.
The magnetic field in a toroid is give by: [itex]B = \frac{\mu_0 n I}{2\pi r}[/itex] Energy stored is given by: [tex]W = {1\over 2\mu_0}\int B^2 d\tau[/tex] [tex]W = {1\over 2\mu_0} \frac{\mu_0^2 n^2 I^2}{4\pi^2}\int {1\over r^2}d\tau[/tex] How do I determine the volume element for a toroid? 


#2
Mar306, 08:21 AM

Sci Advisor
HW Helper
PF Gold
P: 2,014

The toroid can usually be approximated by a solenoid of length 2\pi R,
with r constant inside the toroid. Then V=(2\pi L)*(\pi a^2), with B constant. 


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