In a probe that uses the Hall effect to measure magnetic...

In a probe that uses the Hall effect to measure magnetic fields, a 12.0-A current passes through a 1.50 -cm-wide 1.30-mm-thick strip of sodium metal. If the Hall emf is $1.86 \mu \mathrm{V},$ what is the magnitude of the magnetic field (take it perpendicular to the flat face of the strip)? Assume one free electron per atom of $\mathrm{Na}$, and take its specific gravity to be 0.971 .

Key Concepts

Magnetic Field Measurement

Magnetic field measurement using the Hall effect involves determining the strength of a magnetic field by analyzing the Hall voltage generated in a current-carrying material. The magnitude of this voltage is directly related to the magnetic field, current, and the geometry and carrier density of the material. This technique is particularly useful for non-invasive and precise assessments of magnetic field strengths in various scientific and engineering applications.

Charge Carrier Density

Charge carrier density refers to the number of free charge carriers, such as electrons, per unit volume in a material. In conductive materials like metals, understanding the density of these carriers is crucial for calculating electrical properties, including conductivity and the Hall coefficient. It is often determined using material properties such as specific gravity and atomic structure, which indicate how many free electrons are available to contribute to electrical conduction.

Hall Effect

The Hall effect is a fundamental phenomenon observed when a current-carrying conductor or semiconductor is placed in a magnetic field perpendicular to the current. Due to the Lorentz force, the charge carriers (electrons or holes) experience a force that causes them to accumulate on one side of the material, creating a transverse voltage known as the Hall voltage. This effect is widely used for measuring magnetic fields and characterizing materials based on their charge carrier properties.

Transcript

00:01 Hi there, so for this problem we are given a current that is equal to 12 emperors.

00:07 Also, we are given the width of this that let's label that d and that is equal to 1 .5 centimeters.

00:16 The thickness of this is also given that is 1 .3 millimeters.

00:22 That in meters is equal to 1 .3 times 10 to the minus 3 meters.

00:28 The whole nph also given, and that is equal to 1 .86 micro, which means 10 times 10 to minus 6 bowls.

00:45 And so the question is, what is the magnitude of the magnetic field? take it perpendicular to the flat phase of the strip.

00:54 So we need to determine that magnetic field.

00:57 Also, we need to assume that one free electron per atom of sodium and take its specific gravity.

01:06 So that specific gravity is equal to 0.

01:16 Yes, 0 .0.

01:19 So the specific gravity for this for sodium is equal to 0 .971 times the density.

01:31 Of water, of course, because it is the specific gravity, okay? so remember that this should be then 0 .971 times the density for water, that is 1 ,000 in units of kilometers per cubic meter.

01:48 Now, to determine the electron density, we divide the density of sodium by its atomic weight.

01:57 Now, this gives the number of moles of sodium per cubic meter.

02:01 Multiplying the result by the apple grader number gives the number of subbing atoms per cubic meter.

02:08 Since there is one free electron per atom, this is also the density of free electrons.

02:13 So we proceed like that.

02:15 First of all, we start with the magnetic field.

02:20 That is the whole nph divided by the drift velocity, and this times the width...

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