Shrinking Loop. A circular loop of flexible iron wire has an...

Shrinking Loop. A circular loop of flexible iron wire has an initial circunference of $165.0 \mathrm{cm},$ but its circunference is decreasing at a constant rate of 12.0 $\mathrm{cm} / \mathrm{s}$ due to a tangential pull on the wire. The loop is in a constant, viniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 $\mathrm{T}$ . (a) Find the emf induced in the loop at the instant when 9.0 s have passed. (b) Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

Key Concepts

Faraday's Law of Induction

Faraday's law of induction establishes that a changing magnetic flux through a circuit will induce an electromotive force (emf) in that circuit. This principle is fundamental to understanding how electrical energy is generated from mechanical changes, as seen in devices like generators and transformers.

Magnetic Flux

Magnetic flux is the measure of the total magnetic field passing perpendicularly through a given area. It quantifies the amount of magnetic field linking with a surface and is central to calculating induced emf when the area or the field changes over time.

Rate of Change of Area

The rate of change of area is critical when the geometry of a conducting loop changes over time, as this alters the magnetic flux even if the magnetic field itself remains constant. This concept is applied to calculate how quickly the flux is changing, which in turn affects the induced emf according to Faraday's law.

Lenz's Law

Lenz's law provides the direction of the induced current generated by a changing magnetic flux. It states that the induced current will flow in such a way that its own magnetic field opposes the initial change in flux, thereby ensuring the conservation of energy in electromagnetic systems.

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