A thin-walled insulating tube of radius carries a uniform

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 thin-walled insulating tube of radius

R = 1.5\ \mathrm{cm}

carries a uniform, stationary surface charge density

\sigma = +8.0\ \mathrm{nC\,m^{-2}}

on its wall (a stationary charge carries no current). Over the tube,

2000

turns of thin insulated wire are wound closely and uniformly along a length of

0.40\ \mathrm{m}

, and the wire carries a steady current of

0.60\ \mathrm{A}

. The wire itself is uncharged. Treat the winding as an infinitely long solenoid, so that the field outside it is negligible, and work at points far from the ends. The leads' own fields are ignored. ((a)) Find the magnitude of the magnetic field inside the tube, naming the Ampèrian loop you use and the symmetry that lets you take

B

as constant along part of it. ((b)) Find the magnitude of the electric field at a distance

s = 3.0\ \mathrm{cm}

from the axis. ((c)) Find the magnitude of the electric field at

s = 1.0\ \mathrm{cm}

from the axis. ((d)) An electron inside the tube, at

s = 1.0\ \mathrm{cm}

, moves at

2.0\times10^{6}\ \mathrm{m\,s^{-1}}

radially outwards, i.e. perpendicular to the axis. Find the magnitude of the magnetic force on it.

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