# Magnetostatics - magnetic flux and energy in toroidal inductor

1. Apr 27, 2009

### tigger88

1. The problem statement, all variables and given/known data
A toroidal inductor consists of 500 turns of wire on a ring-shaped core of magnetic material with a relative permeability of 8000. The core has a square cross-section with an internal radius of 20mm, external radius of 40mm and height of 20mm.
Find:
a) Magnetic flux in the core
b) Magnetic energy stored in the inductor
when the current in the winding is 50mA

2. Relevant equations
Magnetic flux = $$\int\int$$B.dS
(1) B = $$\mu$$0$$\mu$$r H
(2) H = (NI)/(2$$\pi$$R)
Ampere's Law: $$\int$$B.dL = $$\mu$$0 I

Energy Um = (1/2)I$$\Phi$$

3. The attempt at a solution
a) From (1) and (2), B = $$\mu$$0$$\mu$$r (NI)/(2$$\pi$$R)
where R is the radius from the centre of the torus to the centre of the core.
Magnetic flux = $$\Phi$$ = B $$\int\int$$dS = $$\mu$$0$$\mu$$r (NI)/(2$$\pi$$R) (2$$\pi$$R)(4h)
= $$\mu$$0$$\mu$$rNI(4h)
Plugging in $$\mu$$r = 8000, I = 50 x 10-3, N = 500, h = 20 x 10-3 gives $$\Phi$$=0.0201Wb

Is this right? If not, where did I go wrong, how do I fix it?

b) Um = (1/2)(50 x 10-3)(0.0201) = 5.03 x 10-4 J

Again, is this right? I'm not comfortable with this course at all. If it's incorrect, how do I fix it? What do I do?