A rectangle measuring 30.0 cm by 40.0 cm is located inside a...

A rectangle measuring 30.0 cm by 40.0 cm is located inside a region of a spatially uniform magnetic field of 1.25 T, with the field perpendicular to the plane of the coil ($\textbf{Fig. E29.26}$). The coil is pulled out at a steady rate of 2.00 cm/s traveling perpendicular to the field lines. The region of the field ends abruptly as shown. Find the emf induced in this coil when it is (a) all inside the field; (b) partly inside the field; (c) all outside the field.

Key Concepts

Magnetic Flux

Magnetic flux is the measure of the magnetic field passing through a given area. It is defined as the product of the magnetic field strength and the component of the area perpendicular to the field. In contexts where the area or the field changes with time, the magnetic flux also changes, which is critical in understanding how electromagnetic induction occurs.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a changing magnetic flux through a loop induces an electromotive force (emf) in that loop. The magnitude of the induced emf is directly proportional to the rate at which the magnetic flux changes. This principle forms the basis for technologies ranging from electric generators to transformers.

Uniform Magnetic Field

A uniform magnetic field has the same magnitude and direction at every point. This simplifies the calculation of magnetic flux because the field strength remains constant over the area of the loop. It is a common idealization used to analyze problems in electromagnetism where spatial variations in the magnetic field are negligible.

Motional Electromotive Force (emf)

Motional emf refers to the emf induced when a conductor or loop moves through a magnetic field, or equivalently, when the area of the loop within the magnetic field changes over time. This concept combines the effects of the geometry of the loop, its motion, and the magnetic field to determine the resultant induced voltage, as governed by Faraday's Law.

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