= Solution
A closed conducting coil linked by a changing <magnetic flux> develops an <electromotive force>. For $N$ turns, <Faraday's law of induction> gives
$$
\boxed{\mathcal E=-N\frac{d\Phi_B}{dt},\qquad
\Phi_B=\int_S\mathbf B\cdot d\mathbf S.}
$$
With a permanent steel magnet, connect the coil to a sensitive <galvanometer> and move a pole into or out of it. Entry and withdrawal give opposite deflections; exchanging the pole reverses the signs. Holding both magnet and coil stationary gives no sustained induction merely because a magnetic field is present. Moving the coil instead, or changing its orientation, can produce the same necessary flux change.
Earth's <magnetic field> can serve as the field source. Turn a many-turn coil so that its area normal changes direction relative to the terrestrial field. In an approximately uniform field, a steadily rotating coil has
$$
\Phi_B=BA\cos\omega t,\qquad
\boxed{\mathcal E=NBA\omega\sin\omega t.}
$$
Reversing a coil from one normal orientation to the opposite changes its flux linkage by $2NBA$. The Earth's weak field calls for an appropriate coil area, number of turns and detector sensitivity; it does not require a chemically supplied current in the detecting circuit. Faraday described terrestrial magneto-electric induction in his Second Series.<Experimental Researches in Electricity, Volume 1 by Michael Faraday>[Second Series, §5: terrestrial magneto-electric induction]{ref}
The coil must provide a conducting return path for a circulating current. Its <electrical resistance> and <self-inductance> affect the response. <Lenz's law> fixes the sign: the induced effect opposes the change responsible for it. The moving system supplies mechanical work when current delivers energy or dissipates heat; a permanent magnet is not thereby an inexhaustible fuel.
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