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Magnetic flux is a fundamental concept in electromagnetism that describes the total magnetic field passing through a specified area. This concept is essential to understanding electromagnetic induction. Magnetic flux, denoted as \( \Phi \), is calculated by the equation \( \Phi = B \cdot A \cdot \cos(\theta) \). Here, \( B \) is the magnetic flux density, \( A \) is the area through which the field lines pass, and \( \theta \) is the angle between the field lines and the normal (perpendicular) to the surface.

In the context of the given exercise, the coil initially has its normal parallel to the magnetic field. As the coil rotates to a position perpendicular to the magnetic field, the angle \( \theta \) changes from 0° to 90°. This change alters the magnetic flux through the coil because the component of the magnetic field passing through the area diminishes.

The change in magnetic flux is directly related to the induced electromotive force (EMF), as captured by Faraday's Law of Induction.

Electromotive Force, commonly abbreviated as EMF, is a measure of the energy provided by a source of electrical current. Although it's called a 'force,' it is more accurately described as a potential difference or voltage. When we speak of EMF in electromagnetic induction, we refer to the voltage generated by a changing magnetic field.

In the scenario of the coil rotating in a magnetic field, the EMF is generated because the coil cuts through magnetic field lines. According to the formula derived in the step-by-step solution, the EMF induced can be determined by the relationship \( Q = \frac{\text{EMF}}{R} \), where \( Q \) is the electrical charge passed through the circuit, and \( R \) is the coil's resistance.

This relationship highlights how the movement within the field results in a measurable potential difference across the coil, allowing us to calculate the strength of EMF (expressed in volts) induced by the changes in magnetic flux.

Faraday's Law of Induction is a key principle in electromagnetism that quantifies how a change in magnetic flux induces an electromotive force (EMF) in a closed circuit. This law is mathematically expressed as \( \text{EMF} = -N \frac{\Delta \Phi}{\Delta t} \), where \( N \) is the number of turns in the coil, \( \Delta \Phi \) is the change in magnetic flux, and \( \Delta t \) is the time interval over which the change occurs.

This law underpins the behavior observed in the exercise, where the coil's rotation through 90 degrees changes the magnetic flux through the coil. Consequently, an EMF is induced, causing a current to flow. The negative sign in the equation represents Lenz's Law, which states that the induced EMF will always oppose the change in flux, striving to counteract it.

By applying Faraday's Law, one can understand how variations in flux lead to the production of electrical currents, crucial for technologies like electric generators and transformers.

Resistance is the measure of how strongly an object opposes the flow of electric charge. Its unit is the ohm (\( \Omega \)). In the context of the rotating coil, resistance plays a critical role in determining how much current flows when EMF is induced.

The relationship between resistance, EMF, and current is given by Ohm's Law: \( V = IR \), where \( V \) is voltage (or EMF in this case), \( I \) is current, and \( R \) is resistance. This law is visible in the step-by-step solution, where the EMF is calculated from the flowing charge and the coil's resistance: \( \text{EMF} = Q \times R \).

Understanding resistance is vital to predicting how much induced current will appear for a given EMF, and it shows how energy loss to heat is inevitable when current flows through the resistance of a conductor. In practical applications, managing resistance ensures efficient energy use.