A long air-cored solenoid is wound with turns per metre

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 long air-cored solenoid is wound with

n = 2000

turns per metre. A small flat coil of

N = 80

turns, each of area

A = 2.5\,\mathrm{cm^2}

, sits well inside the solenoid with its plane perpendicular to the solenoid's axis. The solenoid is long enough that its interior field may be taken as the uniform value

B = \mu_0 n I

over the whole of the small coil, and the coil is connected to a voltmeter of such high resistance that no appreciable current flows in it. ((a)) Calculate the mutual inductance

L_{12}

of the pair. ((b)) The solenoid current is ramped up steadily at

250\,\mathrm{A\,s^{-1}}

. Find the magnitude of the emf induced in the small coil. ((c)) The solenoid's own self-inductance is

L = 3.0\,\mathrm{mH}

. Find the energy stored in it when it carries a steady current of

4.0\,\mathrm{A}

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