What is the Faraday’s Law of Induction?

Question

BlackTom AI · Accepted Answer

Starting with a broad view on Faraday’s Law of Induction, we assess what the law actually states about how emf is generated in a circuit.
Option a: 'The induced emf is directly proportional to the number of loops in the circuit.' While the total emf in a multi-loop circuit can scale with the total flux linkage (which involves both the number of turns and the flux through each turn), Faraday’s Law is more precisely about the time rate of change of magnetic flux, not merely the count of loops. This option misstates the essential dependence on how flux changes, rather than just loop count alone.
Option b: 'The induced emf is directly proportional to the time rate of change of the magnetic flux through the loop.' This aligns with Faraday’s Law: emf equals the negative time derivative of magnetic flux (EMF = -dΦ/dt). It captures the core idea that a changing magnetic environment induces an electric potential, and the faster the flux changes, the larger the induced emf is. This option correctly identifies the central relationship.
Option c: 'The induced current is produced by the magnet bar with the maximum value the magnetic flux through the loop.' This mixes up cause and mechanism. Induced current arises from a changing magnetic flux, not directly from the magnet having a maximum flux value, nor does it specify the rate of change. It also conflates flux magnitude with emf; the sign and magnitude are governed by the time rate of change, not simply the presence of a strong magnet at a given moment.
Option d: 'The induced current is produced by the battery which changes the magnetic flux through the circuit of N loops.' This description attributes induction to a battery-driven flux change, which is inaccurate in standard Faraday-Lenz form. A battery drives current in a circuit, but Faraday’s Law concerns changing magnetic flux due to moving magnets or changing magnetic fields, not due to an internal power source changing flux in the same circuit. It also mentions N loops without tying to the fundamental flux-change mechanism.
In summary, option a partially touches on flux linkage but misses the essential time-rate-of-change dependence; option c and d misidentify the source and mechanism of induction; option b correctly state the core relationship dictated by Faraday’s Law, linking emf to the time rate of change of magnetic flux through the loop.

UCIC 202503 PHYS101 Quiz 11

What is the Faraday’s Law of Induction?

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