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Lenz's Law is a fundamental principle in electromagnetism that describes the direction of induced current resulting from changes in magnetic flux. When a magnetic field through a circuit changes, an electromotive force (emf) is induced. According to Lenz's Law, this induced emf generates a current that flows in a direction that opposes the change in the magnetic flux.

In the context of the circular loop exercise, the magnetic field is pointing into the paper and is constant in magnitude. However, as the loop's diameter is decreasing, the magnetic flux through the loop is also decreasing.

According to Lenz's Law:

• The induced current will flow in a direction such that it tries to keep the original magnetic flux constant.
• Given that the magnetic flux is reducing (since the area of the loop is decreasing), the induced current will generate a field pointing into the paper to oppose the reduction.

This ensures that the magnetic field generated by the induced current acts to counterbalance the diminishing magnetic flux, aligning with Lenz's Law.

Faraday's Law quantifies the induced electromotive force (emf) in a loop resulting from a change in magnetic flux over time. It is given by the equation:

• \[ \varepsilon = - \frac{\Delta \Phi}{\Delta t} \]

Here, \( \varepsilon \) is the induced emf, \( \Delta \Phi \) is the change in magnetic flux, and \( \Delta t \) is the time interval over which this change occurs.

In this scenario, the magnetic flux changes because the area of the circular loop reduces as its diameter decreases from 20 cm to 6 cm. The change in flux \( \Delta \Phi \) was calculated using the formula for the area of a circle \( A = \pi r^2 \), and then applying the flux equation \( \Phi = B \times A \) with a constant magnetic field \( B = 0.75 \, \text{T} \).

The resulting change in flux was used to determine the average induced emf using the equation from Faraday's Law, yielding an emf of \( 0.042855 \, \text{V} \).

Keep in mind that the negative sign in Faraday's Law depicts Lenz's Law, indicating the direction of the induced emf opposes the change in flux.

Ohm's Law is a key principle that relates voltage, current, and resistance in an electrical circuit. It is fundamental for solving problems involving induced current and is expressed as:

• \[ I = \frac{\varepsilon}{R} \]

Where \( I \) is the current, \( \varepsilon \) is the electromotive force or voltage, and \( R \) is the resistance within the circuit.

After calculating the induced emf using Faraday's Law, Ohm's Law helps us find the average induced current in the loop. Given the coil resistance of \( 2.5 \, \Omega \), and the induced emf \( \varepsilon = 0.042855 \, \text{V} \), the induced current is \( 0.017142 \, \text{A} \).

This relation underscores how resistance impacts the induced current, with higher resistance reducing the current flow for a given emf. Understanding and applying Ohm's Law is crucial for completing circuits with varying sources of emf, especially those induced by changing magnetic fields.