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Magnetic flux is a fundamental concept in electromagnetism, representing the quantity of magnetic field passing through a given area. It is denoted by the symbol \( \Phi \), and is calculated by the product of the magnetic field \( B \), the area \( A \), and the cosine of the angle \( \theta \) between them. Mathematically, it is expressed as: \[ \Phi = B \cdot A \cdot \cos(\theta) \]When the magnetic flux passing through a coil changes, it can induce an electromotive force (EMF) in the coil. This principle is the cornerstone of electromagnetic induction, explaining the transformation of magnetic energy into electrical energy.
The flux is measured in webers (Wb), indicating the strength of the magnetic field's influence over the area. A decrease or increase in magnetic flux over time leads to an induced voltage, which is explored further in Faraday's Law.

Faraday's Law of Electromagnetic Induction reveals how changing magnetic flux through a coil induces an electromotive force (EMF). The induced EMF is proportional to the rate at which the magnetic flux changes over time. The formula for Faraday's Law is:\[ \varepsilon = -N \frac{\Delta\Phi}{\Delta t} \]where \( \varepsilon \) is the induced EMF, \( N \) is the number of turns in the coil, \( \Delta\Phi \) is the change in magnetic flux, and \( \Delta t \) is the time interval of the change.
Faraday's Law highlights the importance of the rate of change; a rapid change in flux results in a larger EMF. The negative sign in the equation signifies Lenz's Law, indicating that the induced EMF creates a current that opposes the change in flux.
In this exercise, the change in magnetic flux is calculated, and by applying Faraday's Law, we determine the magnitude of the induced EMF to be 1200 V.

Ohm's Law is a fundamental principle in electrical circuits, expressing the relationship between voltage (V), current (I), and resistance (R). The formula is simple but powerful:\[ V = IR \]This equation tells us that voltage across a conductor is equal to the current flowing through it, multiplied by its resistance. In the context of our problem, the induced EMF acts as the voltage (V). By knowing the current (230 A, as given) and the induced voltage (1200 V), we can solve for the resistance of the wire.
Ohm's Law is crucial for understanding how electrical circuits function, allowing us to determine unknown parameters when two others are known. This aspect of the law is used to calculate the resistance in this scenario, which turns out to be approximately 5.22 ohms.

Induced EMF is at the heart of electromagnetic induction, arising from a change in magnetic flux. The change can be in the magnitude of the magnetic field, the area of the loop, or the orientation of the field with respect to the loop. This induced EMF drives currents in conductors and is the principle underlying devices like transformers and generators.
As calculated using Faraday's Law, the magnitude of the induced EMF is considerable in this exercise, reaching 1200 V due to the swiftly changing magnetic flux in the 12-turn coil. This significant EMF subsequently causes a sizable current of 230 A to flow through the circuit.

• This induced EMF demonstrates how we can convert energy from a changing magnetic field into electrical energy.
• It's essential in many applications, including power generation and electromagnetic braking.

Understanding the concept of induced EMF helps grasp how energy transformations occur seamlessly in electromagnetic systems.