Which, among the following, is the formula for induced emf?

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Examoogle · Accepted Answer

$e = \frac{d\phi}{dt}$

Explanation: Faraday's Law of Electromagnetic Induction states that the magnitude of the electromotive force (emf) induced in a circuit is directly proportional to the rate of change of magnetic flux linking the circuit. Mathematically, it is expressed as the derivative of flux with respect to time.

Working Principle: When the magnetic flux linked with a conductor or coil changes, an electric potential difference or emf is induced. The change in flux can occur due to a varying magnetic field, a moving conductor relative to a stationary field, or a changing area of the loop. According to Faraday's Law, $e = \frac{d\phi}{dt}$, where $e$ is the induced emf and $\frac{d\phi}{dt}$ represents the time-rate of change of magnetic flux.

Key Formulas: $e = \frac{d\phi}{dt}$ — Faraday's Law for induced emf; $e = -N \frac{d\phi}{dt}$ — Lenz's Law form including the number of turns $N$

Key Points: Induced emf depends solely on the rate of change of flux, not the magnitude of flux itself.; Lenz's Law introduces the negative sign, indicating that the induced emf opposes the change in flux that caused it.; Units are Volts (V) for emf and Webers (Wb) for magnetic flux.

Advantages: Fundamental principle for power generation in alternators and generators.; Enables operation of transformers by varying flux in a magnetic core.

Disadvantages: Induced eddy currents can cause significant heating losses in metallic cores.; Flux leakage can reduce the efficiency of induction-based devices.

Applications: Electric Generators (AC/DC); Electrical Transformers; Induction Motors; Electromagnetic Flowmeters

Additional Info: Option B is dimensionally incorrect (seconds per Weber).. Options C and D are products of time and flux, which do not represent emf units (Volts).

Answer: A is correct — The induced emf in a coil is proportional to the time rate of change of the magnetic flux linkage as defined by Faraday's Law.

Exam Tip: Always remember that 'induced emf' is a rate phenomenon; if the magnetic field is constant (static), the change is zero, resulting in zero induced emf in a stationary coil.

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