A toroid is wound with turns of thin insulated wire

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetostatics

Electricity, Magnetism and Electromagnetism, Ch Ampère's law, magnetic flux and the shape of the magnetic field

Problem

A toroid is wound with

N = 1500

turns of thin insulated wire, closely and uniformly spaced, on a non-magnetic core whose inner radius is

3.0\ \mathrm{cm}

and outer radius

5.0\ \mathrm{cm}

. The wire carries a steady current of

0.40\ \mathrm{A}

. ((a)) Find the magnitude of the magnetic field in the core at the inner radius,

s = 3.0\ \mathrm{cm}

, naming the Ampèrian loop and the symmetry that justifies it. ((b)) Find the magnitude of the magnetic field in the core at the outer radius,

s = 5.0\ \mathrm{cm}

. ((c)) A small flat coil of

20

turns, of area

1.0\times10^{-4}\ \mathrm{m^2}

, carrying

50\ \mathrm{mA}

, is held in the core at

s = 4.0\ \mathrm{cm}

with its magnetic moment perpendicular to the local magnetic field. The coil is small enough for the field over it to be treated as uniform. Find the magnitude of the torque on it. ((d)) A point charge of

+3.0\ \mathrm{nC}

is placed inside the core. Find the electric flux out of the closed surface that forms the boundary of the core.

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