In Problem 29, the width of the strip is 3.5 cm, the magnetic field is 0.43 T, the Hall voltag

step 1 In this question, we are given the width, the magnetic field and the whole voltage across the st

In Problem 29, the width of the strip is 3.5 cm, the...

In Problem 29, the width of the strip is $3.5 \mathrm{~cm}$, the magnetic field is $0.43 \mathrm{~T}$, the Hall voltage is measured to be $7.2 \mu \mathrm{V}$, the thickness of the strip is $0.24 \mathrm{~mm}$, and the current in the wire is $54 \mathrm{~A}$. What is the density of carriers (number of carriers per unit volume) in the strip?

Key Concepts

Hall Effect

The Hall effect refers to the generation of a transverse voltage (Hall voltage) in a current-carrying conductor when it is placed in a perpendicular magnetic field. This voltage arises because the magnetic force (Lorentz force) deflects moving charge carriers to one side of the conductor, creating a potential difference that can be measured to determine various material properties.

Charge Carrier Density

Charge carrier density is the number of charge carriers per unit volume in a material. It is a critical parameter in determining the electrical and magnetic behavior of conductors and semiconductors. This density can be inferred from Hall effect measurements by relating the Hall voltage to the applied magnetic field, current, and the geometrical dimensions of the sample.

Lorentz Force

The Lorentz force is the force experienced by a moving charge in the presence of electric and magnetic fields. In the context of the Hall effect, the magnetic component of the Lorentz force causes the deflection of charge carriers, leading to an accumulation on one side of the conductor and the resulting Hall voltage.

Current Density

Current density refers to the amount of electric current flowing per unit area of a conductor. It is an important factor in electromagnetic measurements because it helps determine how the current is distributed within a material, which in turn affects the generation and magnitude of measurable effects like the Hall voltage.

Sample Geometry

The geometrical dimensions of the sample, such as thickness and width, play a vital role in both the distribution of current and the development of the Hall voltage. Accurate knowledge of the sample geometry is essential for interpreting Hall effect measurements and computing intrinsic material properties like carrier density.

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