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A circular loop is a continuous curve that forms the shape of a circle. In the context of electromagnetic induction, the circular loop of wire is an essential component in which an induced electromotive force (EMF) is generated when there is a change in magnetic flux through the loop. For this particular problem, the loop has a radius of 7.50 cm. Converting this into meters, it is 0.075 m. The area of the circular loop, which affects how much magnetic field can interact with it, is calculated using the formula:

• The formula: \( A = \pi r^2 \)
• Plug in the radius: \( A = \pi (0.075)^2 \)
• Result: \( A = 0.0177 \text{ m}^2 \)

This calculation of the area is crucial as it determines the amount of space available for the wave's magnetic field to pass through, which is part of what induces EMF in the loop.

Electromagnetic waves are waves of electric and magnetic fields that propagate through space. These waves can travel through a vacuum, like in air, and have distinct characteristics, such as frequency, wavelength, and intensity. In the given problem, the electromagnetic wave passing through the loop has an intensity of 0.0195 W/m² and a wavelength of 6.90 m.

• Intensity represents the power per unit area and is expressed as \( W/m^2 \).
• The wavelength is the distance between successive peaks of the wave, which is given as 6.90 m.

Understanding these parameters is essential for calculating other properties of the wave, such as the electric and magnetic fields, which in turn influence the induced EMF.

The magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. In the context of electromagnetic waves, the magnetic field is perpendicular to the electric field and the direction of wave propagation. The problem involves calculating the peak magnetic field, \( B_0 \), of the wave interacting with the loop.

• Connected to the peak electric field, \(E_0\), by the formula: \( B_0 = \frac{E_0}{c} \)
• For the electric field \(E_0 = 61.0 \text{ V/m}\), we find:\( B_0 = \frac{61.0}{3.00 \times 10^8} = 2.03 \times 10^{-7} \text{ T} \).

This peak magnetic field is used to compute the maximum induced EMF in the loop.

A sinusoidal wave is a mathematical curve that describes a smooth periodic oscillation. It is a repetitive change or motion in which the amplitude of the wave is described by the sine function. This behavior is typical for electromagnetic waves interacting with a loop of wire in cases like these.

• The wave has a sinusoidal nature, meaning the electric and magnetic fields vary in a sine wave form over time and space.
• Key characteristic: Sinusoidal waves have
  • Amplitude - the 'height' of the wave peaks
  • Frequency - how often the wave oscillates in a second (related to the angular frequency)

Identifying sinusoidal properties allows calculation of meaningful quantities like induced EMF, driven by the change in magnetic field through the loop due to the wave's oscillation.

Induced electromotive force (EMF) is the voltage generated in a circuit due to a change in the magnetic field. According to Faraday's law of electromagnetic induction, an EMF is induced when a conductor experiences a change in magnetic flux. Here, the maximum EMF induced is calculated by considering the loop area, the peak magnetic field, and the angular frequency of the wave.

• Faraday's Law: \( \mathcal{E}_0 = \omega B_0 A \) describes how the rate of change in magnetic flux relates to induced EMF
• For angular frequency: \( \omega = \frac{2\pi c}{\lambda} = 2.73 \times 10^8 \text{ rad/s} \)
• Ensuring all components are known: peak magnetic field \( B_0 = 2.03 \times 10^{-7} \text{ T} \), area \( A = 0.0177 \text{ m}^2 \)

After plugging in these values, the calculated EMF for the current scenario: \( \mathcal{E}_0 = 0.979 \text{ V} \), demonstrating the ability of the setup to convert wave energy into electrical voltage through induction.