A toroid of rectangular cross-section has turns wound tightly and evenly on an…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic induction and alternating-current circuits · Electromagnetic induction and alternating-current circuits

Electricity, Magnetism and Electromagnetism, Ch Self and mutual inductance and magnetic field energy

Problem

A toroid of rectangular cross-section has

N = 800

turns wound tightly and evenly on an air-filled former of inner radius

a = 4.0\,\mathrm{cm}

, outer radius

b = 6.0\,\mathrm{cm}

and height

h = 2.0\,\mathrm{cm}

. The field is taken to be entirely inside the former and circumferential. The winding carries a steady current

I = 3.0\,\mathrm{A}

. ((a)) Using Ampère's law for the field at a distance

s

from the toroid's axis, derive the self-inductance of the toroid and evaluate it. ((b)) Find the energy stored in the toroid at this current. ((c)) A parallel-plate capacitor with vacuum between its plates has a plate separation of

0.50\,\mathrm{mm}

and is charged to

500\,\mathrm{V}

; edge effects are ignored. What plate area would it need in order to store the same energy as the toroid?

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