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Chapter 22: Q30PE (page 812)

A patient with a pacemaker is mistakenly being scanned for an MRI image. A 10.0-cm-long section of pacemaker wire moves at a speed of 10.0 cm/s perpendicular to the MRI unit’s magnetic field and a 20.0-mV Hall voltage is induced What is the magnetic field strength?

Short Answer

Expert verified

The required magnetic field is2.00T

Step by step solution

01

Given information

The diameter of the pacemaker wire is L=10.0cm(1m100cm)=0.1m

The speed of the moving wire isv=10.00cm/s(1m100cm)=0.1m/s

Induced Hall voltage isE=20.0mV(103V1mV)=2.00×10-2V

02

Define the Hall effect

The Hall effect defines the generation of induced voltage due to the motion of charge carriers in a perpendicular applied magnetic field and can be defined as,

E=BLv…………………(1)

03

Evaluating the magnetic field

Substitute the given data in equation (1), which will result,

B=ELv=2.00×10-2V(0.1m)×(0.1m/s)=2.00T

Therefore, the required magnetic field is2.00T

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Most popular questions from this chapter

Frustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a\({\rm{0}}{\rm{.500}}\;{\rm{V}}\)output for blood moving at\({\rm{30}}{\rm{.0 cm/s}}\)in a\({\rm{1}}{\rm{.50}}\;{\rm{cm}}\)diameter vessel. (a) What magnetic field strength is needed? (b) What is unreasonable about this result? (c) Which premise is responsible?

A charged particle having mass \({\rm{6}}{\rm{.64 \times 1}}{{\rm{0}}^{{\rm{ - 27}}}}{\rm{\;kg}}\) (that of a helium atom) moving at \({\rm{8}}{\rm{.70 \times 1}}{{\rm{0}}^{\rm{5}}}{\rm{\;m/s}}\) perpendicular to a \({\rm{1}}{\rm{.50 - T}}\) magnetic field travels in a circular path of radius \({\rm{16}}{\rm{.0\;mm}}\).(a)What is the charge of the particle?(b)What is unreasonable about this result?(c)Which assumptions are responsible?

(a) A 0.750-m-long section of cable carrying current to a car starter motor makes an angle of 60º with the Earth’s 5.50×10‐5field. What is the current when the wire experiences a force of 7.00×10‐3? (b) If you run the wire between the poles of a strong horseshoe magnet, subjecting 5.00 cm of it to a 1.75-T field, what force is exerted on this segment of wire?

A 200-turn circular loop of radius50.0cmis vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. The Earth's field here is due north, parallel to the ground, with a strength of 3.00×10‐5T. What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?

A cosmic ray electron moves at\({\rm{7}}{\rm{.50 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{ m/s}}\)perpendicular to the Earth’s magnetic field at an altitude where field strength is\({\rm{1}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{ T}}\). What is the radius of the circular path the electron follows?
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