A long, tightly wound, air-cored solenoid has turns over a length and a…

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, tightly wound, air-cored solenoid has

N = 1200

turns over a length

l = 30\,\mathrm{cm}

and a cross-sectional area

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

. Treat it as ideal: the field is uniform inside, zero outside, and end effects are ignored. It carries a steady current

I = 2.5\,\mathrm{A}

. ((a)) Starting from Ampère's law for the field inside a long solenoid, derive the self-inductance and evaluate it. ((b)) Find the energy stored in the solenoid at this current. ((c)) A parallel-plate capacitor has plates of area

0.25\,\mathrm{m^2}

separated by

0.10\,\mathrm{mm}

of vacuum, with edge effects ignored. To what potential difference must it be charged so that it stores the same energy as the solenoid?

Browse the problem library