(II) The Hall effect can be used to measure blood flow rate...

(II) The Hall effect can be used to measure blood flow rate because the blood contains ions that constitute an electric current. $(a)$ Does the sign of the ions influence the emf? (b) Determine the flow velocity in an artery 3.3 $\mathrm{mm}$ in diameter if the measured emf is 0.13 $\mathrm{mV}$ and $B$ is 0.070 $\mathrm{T}$ . (In actual practice, an alternating magnetic field is used.)

(II) The Hall effect can be used to measure blood flow rate
because the blood contains ions that constitute an electric
current. $(a)$ Does the sign of the ions influence the emf? (b) Determine the flow velocity in an artery 3.3 $\mathrm{mm}$ in
diameter if the measured emf is 0.13 $\mathrm{mV}$ and $B$ is 0.070 $\mathrm{T}$ .
(In actual practice, an alternating magnetic field is used.)

Key Concepts

Flow Velocity Measurement in Conductive Fluids

The relationship between the induced emf, magnetic field strength, and the velocity of the moving conductor or fluid allows for the determination of flow velocity. By measuring the voltage generated via the Hall effect in a conductive fluid, and knowing the other factors involved, one can calculate the speed at which the fluid is moving. This principle is widely used in various applications, including biomedical measurements and industrial flow monitoring.

Charge Carriers and Ion Sign

In conductive media such as blood, which contains ions, the electric current is carried by both positive and negative ions. Although the sign of the ion determines the direction in which it is deflected by a magnetic field, the overall magnitude of the induced Hall voltage is independent of the charge sign. The separation of charges still produces a measurable emf regardless of whether the moving ions are positive or negative.

Hall Effect

The Hall effect is a physical phenomenon whereby a transverse voltage (or electromotive force) develops across a conductor or semiconductor when a magnetic field is applied perpendicular to the current flow. This effect occurs due to the deflection of charge carriers, which causes a separation of positive and negative charges across the material. It is a key principle in sensor applications and is used to measure magnetic fields and charge carrier dynamics.

Electromotive Force (emf)

Electromotive force (emf) is the voltage generated by the movement of charge carriers within a conductor subjected to external forces such as a magnetic field. In the context of the Hall effect, the emf is induced as a result of the Lorentz force acting on the charge carriers, which deflects them and causes a potential difference across the material.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in a magnetic field, and it acts perpendicular to both the velocity of the particle and the magnetic field. This force is central to the mechanism of the Hall effect, as it causes the deflection of charged particles, leading to charge accumulation on one side and the development of a measurable voltage across the conductor.

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