A long air-cored solenoid wound with turns per metre carries a steady current 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 long air-cored solenoid wound with

n = 1500

turns per metre carries a steady current of

6.0\,\mathrm{A}

. A small open-circuited coil of

N = 25

turns, each of area

A = 8.0\,\mathrm{cm^2}

, sits well inside the solenoid with its plane perpendicular to the axis, so the uniform interior field

B = \mu_0 n I

threads every turn. ((a)) Calculate the mutual inductance

L_{12}

of the pair. ((b)) The solenoid current is then reduced steadily from

6.0\,\mathrm{A}

to zero in

20\,\mathrm{ms}

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

8.5\,\mathrm{mH}

. How much energy was stored in it before the current was reduced?

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