A single-layer coil is wound with turns of thin wire

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

Electricity, Magnetism and Electromagnetism, Ch The Biot-Savart law and the fields of steady currents

Problem

A single-layer coil is wound with

N = 800

turns of thin wire, spread uniformly over a length

l = 25\ \mathrm{cm}

of a cylindrical former of radius

R = 1.5\ \mathrm{cm}

, and carries a steady current

I = 1.5\ \mathrm{A}

. Treat the winding as a uniform sheet of current on the cylinder (the pitch of the winding and the connecting leads are ignored), and take the field point on the axis. ((a)) Find the magnitude of the magnetic field at the centre of the coil. ((b)) The same 800 turns are now rewound, still uniformly over the same length

25\ \mathrm{cm}

, on a former of radius

3.0\ \mathrm{cm}

, carrying the same

1.5\ \mathrm{A}

. Find the magnitude of the field at the centre. ((c)) Give the ratio (new centre field)/(original centre field).

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