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Chapter 19: Problem 38

The strip in the diagram is used as a Hall probe to measure magnetic fields. (a) What happens if the strip is not perpendicular to the field? Does the Hall probe still read the correct field strength? Explain. (b) What happens if the ficld is in the plane of the strip?

Short Answer

Expert verified
Answer: If the strip is not perpendicular to the magnetic field, the Hall probe will not read the correct field strength, as only the perpendicular component of the magnetic field will contribute to the Hall effect. If the magnetic field is in the plane of the strip, the Hall probe will not be able to measure the magnetic field, as there will be no Hall effect and no voltage difference generated across the strip.

Step by step solution

01

a) Strip not perpendicular to the magnetic field

The Hall probe functions through the Hall effect, where a voltage difference (Hall voltage) is generated across a conductor strip under the influence of a magnetic field. To measure the magnetic field accurately, the magnetic field should be perpendicular to the direction of the current in the strip. If the strip is not perpendicular to the magnetic field, the measured Hall voltage will not provide an accurate reading of the magnetic field strength. This is because only the perpendicular component of the magnetic field to the strip will contribute to the Hall effect and result in a Hall voltage, while the parallel component will not have any influence. Therefore, in such a scenario, the Hall probe will not read the correct field strength.
02

b) Magnetic field in the plane of the strip

When the magnetic field is in the plane of the strip, it means that the magnetic field is parallel to the direction of the current in the strip. As previously mentioned, the magnetic field should ideally be perpendicular to the current to generate a Hall voltage which helps in accurately measuring the magnetic field. However, in this case, since the magnetic field is parallel to the current, there will be no Hall effect and no voltage difference generated across the strip. As a result, the Hall probe will not be able to measure the magnetic field in this configuration.

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Most popular questions from this chapter

Four long parallel wires pass through the corners of a square with side $0.10 \mathrm{m}\(. All four wires carry the same magnitude of current \)I=10.0 \mathrm{A}\( in the directions indicated. Find the magnetic field at point \)R,$ the midpoint of the left side of the square.
Two identical bar magnets lie next to one another on a table. Sketch the magnetic field lines if the north poles are at opposite ends.
An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing Na" ions flows due south through an artery with a diameter of \(0.40 \mathrm{cm} .\) The artery is in a downward magnetic field of \(0.25 \mathrm{T}\) and develops a Hall voltage of \(0.35 \mathrm{mV}\) across its diameter. (a) What is the blood specd (in \(\mathrm{m} / \mathrm{s}\) )? (b) What is the flow rate (in \(\mathrm{m}^{3} / \mathrm{s}\) )? (c) The leads of a voltmeter are attached to diametrically opposed points on the artery to measure the Hall voltage. Which of the two leads is at the higher potential?

Two identical long straight conducting wires with a mass per unit length of \(25.0 \mathrm{g} / \mathrm{m}\) are resting parallel to each other on a table. The wires are separated by \(2.5 \mathrm{mm}\) and are carrying currents in opposite directions. (a) If the coefficient of static friction between the wires and the table is \(0.035,\) what minimum current is necessary to make the wires start to move? (b) Do the wires move closer together or farther apart?
Two parallel wires in a horizontal plane carry currents \(I_{1}\) and \(I_{2}\) to the right. The wires each have length \(L\) and are separated by a distance \(d\). (a) What are the magnitude and direction of the ficld due to wire 1 at the location of wire \(2 ?\) (b) What are the magnitude and direction of the magnetic force on wire 2 due to this field? (c) What are the magnitude and direction of the field due to wire 2 at the location of wire \(1 ?\) (d) What are the magnitude and direction of the magnetic force on wire 1 due to this field? (e) Do parallel currents in the same direction attract or repel? (f) What about parallel currents in opposite directions?
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