University of Calgary
Faculty of Engineering
Department of Electrical and Computer Engineering
ENEL 475 - Electromagnetic Fields and Applications
Video Assignment #3
Fall Session 2020
Due Date - Wed Dec 9th by 11:59pm
Auxiliary and side (cross-sectional) views of a toroidal inductor made of wires wrapped around a
circular core are shown in the …gure above - the core has a rectangular cross-section. The core is
made up of two ferromagnetic materials with permeabilities of 1 and 2 as indicated. Assume
zero surface current at the interface between the two materials making up the core. The variables
of the toroidal inductor are de…ned as:
N - number of turns of current wrapped around the core
i - current ‡owing in the wire wrapped around the core
a - inner radius of the toroid
b - outer radius of the toroid
h - thickness of the toroid
1
- permeability in region 1 of the core
2
- permeability in region 2 of the core
Page: 1
Answer the following:
1. Derive an expression for the inductance of the given toroidal inductor in terms of the given
parameters, stating and justifying any assumptions you make in the process
2. For the following set of parameters, determine the stored magnetic energy in the inductor
N = 100
h = 3 cm
a = 2 cm
b = 5:4 cm
1
= 8 H= m
2
= 2 H= m
i = 10 A
Page: 2