A solenoid has turns wound uniformly over a length on a non-magnetic former of…

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 solenoid has

2000

turns wound uniformly over a length

l = 0.50\ \mathrm{m}

on a non-magnetic former of circular cross-section of radius

1.5\ \mathrm{cm}

, and carries a steady current

I = 2.5\ \mathrm{A}

. Treat it as a long solenoid: the field inside is uniform and along the axis, and the field outside is negligible. End effects are ignored. ((a)) Starting from the field of a long solenoid and the definition

N\Phi_B = LI

, derive

L = \mu_0 n^2 A l

(with

n

the turns per unit length and

A

the cross-sectional area) and evaluate

L

. ((b)) Evaluate the energy stored,

\tfrac12 L I^2

. ((c)) Evaluate the magnetic energy density

u = B^2/2\mu_0

inside the solenoid, and show that

u

times the interior volume reproduces your answer to (b).

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