A current I=40.0 A flows through a strip of metal. An...

A current $I=40.0 \mathrm{~A}$ flows through a strip of metal. An electromagnet is switched on so that there is a uniform magnetic field of magnitude $0.30 \mathrm{~T}$ directed into the page. (a) How would you hook up a voltmeter to measure the Hall voltage? Show how the voltmeter is connected on a sketch of the strip. (b) Assuming the carriers are electrons, which lead of your voltmeter is at the higher potential? Mark it with " "'" sign in your sketch. Explain briefly.

A current $I=40.0 \mathrm{~A}$ flows through a strip of metal. An electromagnet is switched on so that there is a uniform magnetic field of magnitude $0.30 \mathrm{~T}$ directed into the page.
(a) How would you hook up a voltmeter to measure the Hall voltage? Show how the voltmeter is connected on a sketch of the strip. (b) Assuming the carriers are electrons, which lead of your voltmeter is at the higher potential? Mark it with " "'" sign in your sketch. Explain briefly.

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Key Concepts

Hall Effect

The Hall effect is the production of a transverse voltage in a current-carrying conductor when it is placed in a magnetic field. This voltage is created due to the deflection of moving charge carriers by the magnetic field, which leads to a buildup of charge on one side of the conductor.

Lorentz Force

The Lorentz force is the force that a charged particle experiences when it moves through perpendicular electric and magnetic fields, expressed as F = q(v × B). In the Hall effect, this force causes the charge carriers to move towards one edge of the conductor, creating a measurable potential difference.

Measurement Configuration for Hall Voltage

To measure the Hall voltage, a voltmeter is connected across the width of the conductor, i.e., perpendicular to the current flow. This connection picks up the transverse voltage that results from the separation of charges under the influence of the magnetic field.

Charge Carrier Type and Polarity Consideration

The polarity of the measured Hall voltage depends on the type of charge carriers in the conductor. If the carriers are electrons, which are negatively charged, the direction of the Lorentz force implies that the side of the conductor where electrons accumulate will be at a lower potential, making the opposite side exhibit a higher potential on the voltmeter reading.

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