Magstripe reader A magstripe reader used to read a credit...

Magstripe reader A magstripe reader used to read a credit card number or a card key for a hotel room has a tiny coil that detects a changing magnetic field as tiny bar magnets pass by the coil. Calculate the magnitude of the induced emf in a magstripe card reader coil. Assume that the mags tripe magnetic field changes at a constant rate of 500 mT/ms as the region between two tiny magnets on the stripe passes the coil. The reader coil is 2.0 mm in diameter and has 5000 turns.

Key Concepts

Faraday's Law of Electromagnetic Induction

This principle states that a changing magnetic flux through a closed loop induces an electromotive force (emf) in that loop. The magnitude of the induced emf is proportional to both the rate of change in the magnetic flux and the number of turns in the coil. It is one of the fundamental laws that explains how electrical energy can be generated from changing magnetic fields.

Magnetic Flux

Magnetic flux is the measure of the magnetic field passing through a given area. It depends on the strength of the magnetic field, the area of the loop, and the orientation of the field relative to the loop. In the context of electromagnetic induction, changes in magnetic flux over time lead to the generation of an induced emf according to Faraday’s Law.

Coil Geometry and Area

The geometry of the coil, particularly its area, plays a crucial role in determining the magnetic flux passing through it. A larger coil area results in a higher magnetic flux for a given magnetic field, thereby affecting the magnitude of the induced emf. The area is typically calculated using the formula for the area of a circle when dealing with circular coils.

Rate of Change of the Magnetic Field

The induced emf in a coil is directly related to how quickly the magnetic field changes with time. A constant rate of change implies that the magnetic flux is changing steadily, which allows for straightforward calculation of the induced emf using the relationship provided by Faraday’s Law. This rate of change is a key factor determining the effectiveness of devices that rely on electromagnetic induction.

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