Figure P 25.16 shows a 100 -turn coil of wire of radius 12 cm in a 0.15 T magnetic field. The co

step 1 Hello friends here it is given there is a quay of 100 tons each of radius 12 centimeter is rotat

Figure P 25.16 shows a 100 -turn coil of wire of radius 12...

Figure $P 25.16$ shows a 100 -turn coil of wire of radius $12 \mathrm{cm}$ in a $0.15 \mathrm{T}$ magnetic field. The coil is rotated $90^{\circ}$ in $0.30 \mathrm{s}$, ending up parallel to the field. What is the average emf induced in the coil as it rotates?

Key Concepts

Rate of Change of Flux (Time Dependence)

The magnitude of the induced EMF depends on how quickly the magnetic flux through the coil changes. In scenarios where the coil rotates or the magnetic field changes, the average induced emf is determined by dividing the total change in magnetic flux by the time interval over which the change occurs, highlighting the dynamic aspect of electromagnetic induction.

Coil Geometry and Turn Count

The geometry of the coil, including the area of each loop and the number of turns, directly affects the total magnetic flux linked with the coil. A multiple-turn coil acts as several loops connected in series, so when each loop experiences a change in flux, the total induced emf is the sum of the contributions from each turn.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that an electromotive force (EMF) is induced in a circuit when there is a change in the magnetic flux through the circuit over time. This principle is fundamental in electromagnetism and is the underlying mechanism for devices such as generators and transformers.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It is calculated by multiplying the magnetic field strength by the area through which the field lines pass, taking into account the angle between the field direction and the normal to the surface. Changes in this quantity, due to either variations in the field intensity, the area, or the orientation, lead to the induction of an EMF.

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