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Energy stored in a toroid

by Reshma
Tags: energy, stored, toroid
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Mar3-06, 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?
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Meir Achuz
Mar3-06, 08:21 AM
Sci Advisor
HW Helper
PF Gold
P: 1,992
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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