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I had a question while studying the Hall effect.

After going through various intermediate processes, the Hall coefficient can be derived as follows,

$R_H=\frac{1}{qn},$

where $q$ is the quantity of charge and $n$ is the carrier concentration.

However, I don't understand why the Hall coefficient decreases as the carrier concentration increases.

Intuitively, the higher the carrier concentration, the greater the Hall voltage, so shouldn't the Hall coefficient be higher?

Why are carrier concentration and Hall coefficient inversely proportional?

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For a given current, and all other things being equal, if the charge concentration goes up, Hall coefficient goes down, then the drift speed of the charge carriers goes down.
If the drift speed decreases then the Lorentz force on the charge carriers decreases.
If the Lorentz force decreases then the force on the charge carriers due to the (Hall) electric field decreases.
If the electric field decreases then the Hall voltage decreases.

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