A patient with a pacemaker is mistakenly being scanned for...

A patient with a pacemaker is mistakenly being scanned for an MRI image. $A 10.0-\mathrm{cm}$ -long section of pacemaker wire moves at a speed of 10.0 $\mathrm{cm} / \mathrm{s}$ perpendicular to the MRI unit's magnetic field and a $20.0-\mathrm{mV}$ Hall voltage is induced. What is the magnetic field strength?

Key Concepts

Motional Electromotive Force (EMF)

Motional EMF is the voltage generated when a conductor moves through a magnetic field. It arises because the moving charges in the conductor experience the Lorentz force, which causes a separation of positive and negative charges, creating an electric potential difference along the length of the conductor. The induced EMF can be calculated by multiplying the magnetic field strength (B), the length of the conductor (L), and its velocity (v) perpendicular to the field (EMF = B * L * v).

Lorentz Force

The Lorentz force is the force experienced by charged particles when moving in a magnetic field. It acts perpendicular to both the direction of the particle's motion and the magnetic field, and is responsible for the deflection and subsequent charge separation in a moving conductor. This force is fundamental in explaining how motion in a magnetic field can lead to an induced voltage.

Hall Effect

The Hall effect refers to the generation of a voltage (Hall voltage) across an electrical conductor, transverse to both the current direction and a magnetic field perpendicular to the current. It is a direct demonstration of how the Lorentz force causes charge carriers to accumulate on one side of the conductor, and it provides a method for measuring the magnetic field strength through the relationship between the induced voltage, the speed of charge carriers, and the dimensions of the conductor.

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