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Chapter 22: Problem 4

The drawing shows a type of flow meter that can be used to measure the speed of blood in situations when a blood vessel is sufficiently exposed (e.g., during surgery). Blood is conductive enough that it can be treated as a moving conductor. When it flows perpendicularly with respect to a magnetic field, as in the drawing, electrodes can be used to measure the small voltage that develops across the vessel. Suppose that the speed of the blood is \(0.30 \mathrm{m} / \mathrm{s}\) and the diameter of the vessel is \(5.6 \mathrm{mm} .\) In a \(0.60-\mathrm{T}\) magnetic field what is the magnitude of the voltage that is measured with the electrodes in the drawing?

Short Answer

Expert verified
The voltage measured is approximately 1.008 millivolts.

Step by step solution

01

Understanding the Problem

The problem involves measuring the voltage produced when blood, treated as a conductor, moves through a magnetic field. We're given the speed of the blood, the diameter of the blood vessel, and the strength of the magnetic field. Our task is to calculate the voltage across the blood vessel.
02

Identifying the Relevant Formula

The voltage induced across the blood vessel can be calculated with the formula: \[ V = B imes v imes d \]where \( V \) is the voltage, \( B \) is the magnetic field strength, \( v \) is the speed of the conductor (blood), and \( d \) is the diameter (distance between electrodes).
03

Converting Measurements

First, convert the diameter of the blood vessel from millimeters to meters. The diameter is given as 5.6 mm.\[ d = 5.6 \text{ mm} = 5.6 \times 10^{-3} \text{ m} \]
04

Substituting the Values

Now, substitute the given values into the formula. We have:- \( v = 0.30 \text{ m/s} \)- \( B = 0.60 \text{ T} \)- \( d = 5.6 \times 10^{-3} \text{ m} \)Thus, the calculation for voltage \( V \) is:\[ V = 0.60 \times 0.30 \times 5.6 \times 10^{-3} \]
05

Calculating the Result

Now, compute the product:\[ V = 0.60 \times 0.30 \times 5.6 \times 10^{-3} = 1.008 \times 10^{-3} \text{ V} \]So, the magnitude of the voltage is approximately 1.008 millivolts.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Blood Velocity Measurement
Measuring the velocity of blood is crucial in medical diagnostics. Blood velocity refers to the speed at which blood flows through the body's vessels. In the context of the given exercise, a magnetic flow meter is used to determine this speed, by measuring the voltage generated when blood moves through a magnetic field.
In surgical settings, accurate measurement of blood velocity ensures proper monitoring of patient health. It allows doctors to assess blood flow under various conditions. A high blood velocity can indicate potential issues such as hypertension, while low velocity may indicate blockages or other circulatory problems.
By understanding the blood velocity, doctors can make informed decisions about medical treatments. This enhances patient care and leads to better health outcomes.
Magnetic Field
A magnetic field is a region around a magnetic material or a moving electric charge within which the force of magnetism acts. In the context of the magnetic flow meter, it's essential in the measurement process.
The magnetic field in the meter is typically represented by the symbol \( B \) and is usually measured in Teslas (T). Within this context, the blood, acting as a conducting fluid, moves perpendicularly through the magnetic field, facilitating the generation of a voltage.
This alignment is crucial as it maximizes the voltage induced across the electrodes. If the blood doesn't move perpendicularly, the alignment of the magnetic field needs adjustment to ensure accurate readings. Thus, understanding how magnetic fields interact with moving charges is foundational in using magnetic flow meters effectively.
Induced Voltage
The principle of induced voltage is what underlies the function of magnetic flow meters. According to Faraday's law of electromagnetic induction, a voltage can be induced in a conductor when it moves through a magnetic field.
In this exercise, the movement of conductive blood through a static magnetic field causes an electrical voltage to form across the vessel. This induced voltage \( V \) can be calculated using the formula \( V = B \times v \times d \), where \( B \) is the magnetic field strength, \( v \) is the velocity of the blood, and \( d \) is the distance across which the voltage is measured (the diameter of the blood vessel).
This voltage can be very small, often in millivolts, but it provides a direct measure of the blood velocity when correctly interpreted. By employing properly positioned electrodes, healthcare professionals can harness this principle to measure blood flow accurately and noninvasively.
Electrodes in Medical Instruments
Electrodes are key components in various medical instruments. They are used to detect electrical voltages and currents related to physiological processes. In a magnetic flow meter, electrodes measure the tiny voltage generated by the blood moving through the magnetic field.
Electrodes must be positioned carefully within the vessel to ensure they capture the induced voltage accurately. They need to maintain excellent contact with the area of interest鈥攊n this case, the blood vessel鈥攖o ensure accurate measurements. Often, these electrodes are made from biocompatible materials, ensuring they do not cause adverse reactions while in contact with bodily fluids.
The efficient use of electrodes allows for precise monitoring and measurement of physiological parameters such as blood flow. This technological advancement aids health professionals in obtaining reliable data to make critical medical decisions.

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Most popular questions from this chapter

A motor is designed to operate on \(117 \mathrm{V}\) and draws a current of \(12.2 \mathrm{A}\) when \(\mathrm{it}\) first starts up. At its normal operating speed, the motor draws a current of 2.30 A. Obtain (a) the resistance of the armature coil, (b) the back emf developed at normal speed, and (c) the current drawn by the motor at one-third of the normal speed.

A flat coil of wire has an area \(A, N\) turns, and a resistance \(R\). It is situated in a magnetic field, such that the normal to the coil is parallel to the magnetic field. The coil is then rotated through an angle of \(90^{\circ},\) so that the normal becomes perpendicular to the magnetic field. The coil has an area of \(1.5 \times 10^{-3} \mathrm{m}^{2}, 50\) turns, and a resistance of \(140 \Omega .\) During the time while it is rotating, a charge of \(8.5 \times 10^{-5} \mathrm{C}\) flows in the coil. What is the magnitude of the magnetic field?

Indicate the direction of the electric field between the plates of the parallel plate capacitor shown in the drawing if the magnetic field is decreasing in time. Give your reasoning.

The plane of a flat, circular loop of wire is horizontal. An external magnetic field is directed perpendicular to the plane of the loop. The magnitude of the external magnetic field is increasing with time. Because of this increasing magnetic field, an induced current is flowing clockwise in the loop, as viewed from above. What is the direction of the external magnetic field? Justify your conclusion.

Suppose there are two transformers between your house and the high-voltage transmission line that distributes the power. In addition, assume that your house is the only one using electric power. At a substation the primary coil of a step-down transformer (turns ratio \(=1: 29\) ) receives the voltage from the high-voltage transmission line. Because of your usage, a current of \(48 \mathrm{mA}\) exists in the primary coil of this transformer. The secondary coil is connected to the primary of another step-down transformer (turns ratio \(=1: 32\) ) somewhere near your house, perhaps up on a telephone pole. The secondary coil of this transformer delivers a \(240-\mathrm{V}\) emf to your house. How much power is your house using? Remember that the current and voltage given in this problem are rms values.
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