Calculate the Hall voltage induced on a patient's heart...

Calculate the Hall voltage induced on a patient's heart while being scanned by an MRI unit. Approximate the conducting path on the heart wall by a wire 7.50 $\mathrm{cm}$ long that moves at 10.0 $\mathrm{cm} / \mathrm{s}$ perpendicular to a 1.50 -T magnetic field.

Key Concepts

Motional Electromotive Force (EMF)

Motional EMF refers to the voltage induced in a conductor when it moves through a magnetic field. The movement causes a change in magnetic flux through the conductor, resulting in the separation of electric charges due to the Lorentz force. This induced voltage is central to understanding phenomena where motion in a magnetic field gives rise to observable electrical effects.

Hall Effect

The Hall effect is the generation of a measurable transverse voltage (Hall voltage) across an electrical conductor when it carries current in the presence of a perpendicular magnetic field. This effect occurs because the magnetic force deflects the charge carriers, causing them to accumulate on one side of the conductor, thereby establishing a potential difference.

Lorentz Force

The Lorentz force is the force exerted on charged particles moving within a magnetic field. In a moving conductor, this force acts on the free charge carriers, causing them to move or deflect, which leads to the separation of charges and the development of an induced voltage across the conductor.

Magnetic Field

A magnetic field is a spatial region where magnetic forces are exerted on moving charges or magnetic materials. In many practical applications, such as MRI machines, strong magnetic fields interact with moving conductors to produce effects like motional EMF and the Hall effect, which are essential for both imaging technologies and sensors.

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