91Ó°ÊÓ

Faraday's Law of electromagnetic induction is a fundamental principle that describes how an electric field is generated by a changing magnetic field. This law states that the induced electromotive force (emf) in any closed circuit is equal to the rate of change of the magnetic flux through the circuit. In mathematical terms, Faraday's Law can be expressed as:
\[ ext{emf} = -N \frac{d ext{Φ}_m}{dt} \]where:

• \( N \): Number of turns in the coil
• \( ext{Φ}_m \): Magnetic flux
• \( \frac{d ext{Φ}_m}{dt} \): Rate of change of magnetic flux

In our exercise, Faraday's Law is used to calculate the maximum induced emf when the coil rotates at a certain speed in the magnetic field. The formula simplifies to \( ext{emf} = NAB\omega \) for a coil rotating uniformly, where:

• \( A \): Area of the coil, obtained from its radius
• \( B \): Magnetic field strength
• \( \omega \): Angular speed of rotation

By applying these principles correctly, we find that a maximum emf of 0.60 V is induced in the coil.

Joule Heating, also known as resistive or ohmic heating, refers to the process where the electric current passing through a conductor produces thermal energy (heat) due to the resistance. The amount of heat produced can be determined by the formula:
\[P = I^2 R\]where:

• \( P \): Power (heat) produced
• \( I \): Current through the conductor
• \( R \): Resistance of the conductor

In the problem at hand, we calculate the average power loss due to Joule heating in the coil by using the maximum current and resistance. Since the current varies sinusoidally in this setup, the average power can also be determined using:
\[P_{avg} = \frac{1}{2} \varepsilon_{max} I_{max}\]In this instance, with a resistance of 10 Ω and a maximum current of 0.06 A, the average power loss due to Joule heating is found to be 0.018 W. This formula shows how resistance can convert electrical energy into heat, emphasizing the importance of resistor efficiency in electronic devices.

Ohm's Law is a fundamental principle that describes the relationship between voltage, current, and resistance in an electrical circuit. It is expressed by the equation:
\[V = IR\]where:

• \( V \): Voltage across the conductor
• \( I \): Current flowing through the conductor
• \( R \): Resistance of the conductor

In our context, Ohm's Law is instrumental in determining the maximum current (\( I_{max} \)) that flows through the coil when the maximum emf (\( \varepsilon_{max} \)) is induced. By rearranging the formula, we find that:
\[I_{max} = \frac{\varepsilon_{max}}{R}\]This calculation shows how voltage applied to a circuit and resistance within that circuit determines the current. For this exercise, with \( \varepsilon_{max} = 0.60 \, V \) and resistance \( R = 10 \, \Omega \), the resultant maximum current is 0.06 A. Understanding Ohm's Law helps in predicting how circuits will respond to changing electrical conditions.