An aluminium wire of uniform cross-sectional area and conductivity carries a steady…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Electric current and circuits

Electricity, Magnetism and Electromagnetism, Ch Current, current density, conductivity and Ohm's law

Problem

An aluminium wire of uniform cross-sectional area

2.5\,\mathrm{mm^2}

and conductivity

\sigma_{\mathrm{c}} = 3.5\times10^{7}\,\mathrm{S\,m^{-1}}

carries a steady current of

8.0\,\mathrm{A}

. The wire is bent through a right angle at one point. Take the current density as uniform over the cross-section, and treat the material just outside the wire as vacuum. ((a)) Find the magnitude of the electric field inside the metal. ((b)) At the bend the field must be turned through

90^\circ

. Use the Chapter 4 result for the field just outside a conductor's surface to estimate the extra surface charge density needed there, of order

\varepsilon_0 E

. ((c)) Express this as a number of elementary charges per square millimetre. ((d)) The whole wire is

1.6\,\mathrm{m}

long. What potential difference must the cell maintain between its two ends to keep this current flowing?

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