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Faraday's Law of Electromagnetic Induction is crucial in understanding how electric currents are generated. It tells us that a changing magnetic field can induce an electromotive force (emf) in a coil. This law can be mathematically expressed as \( E = - N \frac{\Delta \Phi}{\Delta t} \), where:

• \( E \) 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 during which the change occurs.

The negative sign in the formula signifies Lenz’s Law, indicating that the induced emf will generate a current whose magnetic field opposes the change in flux. In simpler terms, Faraday's Law shows how moving a magnet through a coil can light up a bulb, by turning mechanical energy into electrical energy. In the given problem, the magnetic flux decreases, so the direction of the induced emf is such that it will oppose this decrease, according to Lenz's Law.

Ohm's Law is a foundational principle in electrical circuits. It states the relationship between voltage \( V \), current \( I \), and resistance \( R \) in an electrical circuit, given by the formula:

• \( V = IR \)

This formula can be rearranged depending on what we need to find:

• To find voltage: \( V = IR \)
• To find current: \( I = \frac{V}{R} \)
• To find resistance: \( R = \frac{V}{I} \)

In the exercise, the induced emf (calculated using Faraday’s Law) acts as the voltage, and the given current allows us to determine the coil's resistance. This is a perfect real-world example of how Ohm's Law is applied to determine unknown values in an electrical circuit.

Magnetic flux is a measure of the quantity of magnetism, taking into account the strength and the extent of a magnetic field. It's denoted by \( \Phi \) and measured in Weber (Wb). Mathematically, magnetic flux through a surface is described by:

• \( \Phi = B \cdot A \cdot \cos(\theta) \)

where:

• \( B \) is the magnetic field strength,
• \( A \) is the area through which the field lines pass, and
• \( \theta \) is the angle between the magnetic field lines and the perpendicular to the surface.

In the provided problem, the change in magnetic flux (from 9.0 Wb to 4.0 Wb) drives the induced emf across the coil. This change is the heart of what causes the electrical current to flow under Faraday’s law. It not only helps in computing the induced emf but also signifies the interaction between electricity and magnetism.

Coil resistance is the opposition that a coil offers to the flow of electric current. Every coil of wire has some resistance, and it can significantly influence how the coil behaves in a circuit. Resistance is measured in ohms (\( \Omega \)) and can be influenced by various factors, such as:

• The material of the wire,
• The length of the wire, and
• The thickness of the wire.

In our problem, the resistance was calculated using Ohm's Law after determining the induced voltage via Faraday’s Law and the average current through the coil. Understanding coil resistance is vital for designing electrical circuits and ensuring they function as intended. Proper management of resistance ensures that power is delivered efficiently without unnecessary energy loss.