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In medicine, it is often important to monitor the blood flow in certain areas of the body. However, the movement of blood is difficult to monitor directly. Instead, some medical devices use the Hall effect, taking advantage of the fact that the blood flowing through a vein contains a considerable number of free ions.
Model the vein in a patient's arm to be of rectangular cross section, as shown in the figure, with a width w=4.00 mm and height ℎ=3.35 mm. The entire section of the vein is immersed in a constant magnetic field of ?=0.0955 T, pointing horizontally and parallel to the width. A medical device constantly monitors the resulting Hall voltage.
Suppose that medical precautions mandate that the speed of the blood flow for this particular component of the body should never drop below 21.40 cm/s. At what minimum Hall voltage VH, in millivolts, should the medical device be designed to trigger an alarm to the medical staff?
?H=
mV
Transcribed Image Text:**Transcription for Educational Website:**
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**Electromagnetic Flow of Charged Particles in a Conductor**
The diagram illustrates the movement of charged particles within a conductive material subjected to both an electric field and a magnetic field.
**Key Features of the Diagram:**
1. **Charged Particles:**
- **Positive Charges (Protons):** Represented by red circles with a "+" symbol.
- **Negative Charges (Electrons):** Represented by blue circles with a "-" symbol.
2. **Flow Direction (Green Arrows):**
- The green arrows indicate the direction of motion of the charged particles. Both positive and negative charges travel from one end of the conductor to the other within the material.
3. **Magnetic Field (B):**
- Depicted by blue arrows labeled "B," the magnetic field enters the conductor perpendicularly to the plane of motion of the charged particles.
4. **Velocity (v):**
- The parameter "v" on the left side signifies the velocity direction of the moving charged particles within the conductive material.
5. **Dimensions of the Conductor:**
- **Height (h):** The vertical dimension of the rectangular conductor.
- **Width (w):** The horizontal dimension of the rectangular conductor.
- The conductor is shown as a rectangular box, providing a perspective on the space through which the charged particles move.
**Interpretation:**
In this setup, the interaction between the electric current (flow of charged particles) and the magnetic field leads to phenomena such as electromagnetic force and potential differences across various points in the conductor. This foundational concept highlights the principles of electromagnetism and helps understand devices like electric motors, generators, and magnetic field applications in technology.
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**Educational Insight:**
This visual and textual explanation offers insight into how magnetic fields influence the motion of charged particles, emphasizing the fundamental principles of electromagnetism. This is essential for students studying physics and electromagnetic theory.
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