A 25-turn circular coil of wire has a diameter of 1.00 m....

A 25-turn circular coil of wire has a diameter of $1.00 \mathrm{~m}$. It is placed with its axis along the direction of the Earth's magnetic field of $50.0 \mu \mathrm{T}$, and then in $0.200 \mathrm{~s}$ it is flipped $180^{\circ}$. An average emf of what magnitude is generated in the coil?

Key Concepts

Magnetic Flux

Magnetic flux quantifies the number of magnetic field lines passing through a given area. It is calculated as the product of the magnetic field strength, the area through which the field lines pass, and the cosine of the angle between the field direction and the normal (perpendicular) to the surface. This concept is central to predicting the induced emf in a circuit subject to a changing magnetic field.

Faraday's Law of Electromagnetic Induction

This principle states that an electromotive force (emf) is induced in a closed circuit when there is a change in the magnetic flux through the circuit. It is mathematically expressed as emf = -d?/dt, where ? is the magnetic flux. The law provides the foundation for understanding how and why electrical currents can be generated by changing magnetic environments.

Circular Coil Geometry

Understanding the geometry of a coil is crucial because the area enclosed by the coil directly affects the magnetic flux. For a circular coil, the area is determined using the formula A = ?r², where r is the radius. This geometric relationship is vital when calculating the total flux through the coil or when analyzing how changes in orientation impact the flux.

Time Rate of Change of Magnetic Flux

The induced emf depends on how quickly the magnetic flux through a circuit changes with time. This emphasizes the importance of the time interval over which the flux change occurs, as a rapid change produces a larger induced emf compared to a gradual change. The concept links temporal variations to the magnitude of the induced electrical response.

Magnetic Field

A magnetic field represents the region of influence produced by magnetic materials or moving electric charges, characterized by both magnitude and direction. It is the external factor interacting with the coil, and its strength, combined with the coil's orientation and area, determines the magnetic flux and hence the induced emf when altered.

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