A long air-cored solenoid has 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 has

n = 800

turns per metre. A small coil of

N = 120

turns, each of area

A = 6.0\,\mathrm{cm^2}

, lies deep inside it, coaxial with it, so that the uniform interior field

B = \mu_0 n I

threads every turn; the coil is left open-circuited, so it carries no current. ((a)) Calculate the mutual inductance

L_{12}

of the pair. ((b)) At what steady rate must the solenoid current change if the emf induced in the small coil is to be

15\,\mathrm{mV}

? ((c)) The solenoid behaves as an ideal inductor of self-inductance

12\,\mathrm{mH}

. What current does it carry when it stores

0.30\,\mathrm{J}

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