What is the relationship between induced emf and magnetic flux?

Induced emf, or electromotive force, is fundamentally linked to the principle of electromagnetic induction, which states that a changing magnetic flux through a circuit induces an electromotive force in that circuit. According to Faraday's law of electromagnetic induction, the induced emf is directly proportional to the rate of change of magnetic flux through the circuit over time.

When the magnetic flux changes—whether it be due to the motion of a magnet relative to a coil, the coil moving through a magnetic field, or a change in the strength of the magnetic field itself—an emf is induced. The faster this change occurs, the greater the induced emf. The relationship is quantitatively expressed in the formula ( \text{emf} = -\frac{d\Phi}{dt} ), where ( \Phi ) is the magnetic flux. The negative sign indicates the direction of the induced emf as per Lenz's law, which states that the induced emf will act in a direction to oppose the change in flux.

Understanding this principle clarifies why the other options do not accurately describe the relationship: induced emf is not merely a reflection of the magnetic field's strength; it is dependent on how that magnetic field changes over time. Furthermore, induced emf is not