An electrocardiogram (ECG) measures electric activity of neurons in the brain. Electroencephalograms and electromyograms respectively measure similar activity over the scalp and over the skin surrounding muscle cells. Because the electrical activity of the human body varies with time, the time-varying electric fields in the body lead to the generation of magnetic fields that can then be measured. The magnetocardiogram, developed in the 1960s, was the first such device. More recently, superconducting quantum interference devices (SQUIDS) have been used for these measurements. One important application of this technique is the monitoring of the fetal heart by measuring the magnetic field produced by currents in the heart at the surface of the mother's abdomen. The fetal heart at 28 weeks gestation can be modeled as a single-loop coil 1.50 cm in diameter, oriented so that the plane of the loop is parallel to the abdominal surface of the mother, and a magnetic field of 10.0 pT is typically measured by the SQUID. (a) If the distance from the abdominal wall of the mother to the fetal heart is 4.92 cm, what is the magnitude of the current in the heart (in μA) that can produce the measured magnetic field? Assume that the measurement is made directly above and along the axis of the coil representing the fetal heart. 261.6 x What is the fetal heart modeled as? Can any of the equations derived in the text be used to compute the magnetic field of the fetal heart? μA (b) What is the magnetic dipole moment of the fetal heart? (Enter the magnitude in nA m².) nA m2 (c) A magnetic dipole moment of magnitude greater than 15.0 nA m². has been associated with cardiomegaly, an abnormal enlargement of the fetal heart. What would the magnetic field measured by the SQUID have to be for the fetal heart to be considered abnormally large? (Enter the magnitude in pT.)
An electrocardiogram (ECG) measures electric activity of neurons in the brain. Electroencephalograms and electromyograms respectively measure similar activity over the scalp and over the skin surrounding muscle cells. Because the electrical activity of the human body varies with time, the time-varying electric fields in the body lead to the generation of magnetic fields that can then be measured. The magnetocardiogram, developed in the 1960s, was the first such device. More recently, superconducting quantum interference devices (SQUIDS) have been used for these measurements. One important application of this technique is the monitoring of the fetal heart by measuring the magnetic field produced by currents in the heart at the surface of the mother's abdomen. The fetal heart at 28 weeks gestation can be modeled as a single-loop coil 1.50 cm in diameter, oriented so that the plane of the loop is parallel to the abdominal surface of the mother, and a magnetic field of 10.0 pT is typically measured by the SQUID. (a) If the distance from the abdominal wall of the mother to the fetal heart is 4.92 cm, what is the magnitude of the current in the heart (in μA) that can produce the measured magnetic field? Assume that the measurement is made directly above and along the axis of the coil representing the fetal heart. 261.6 x What is the fetal heart modeled as? Can any of the equations derived in the text be used to compute the magnetic field of the fetal heart? μA (b) What is the magnetic dipole moment of the fetal heart? (Enter the magnitude in nA m².) nA m2 (c) A magnetic dipole moment of magnitude greater than 15.0 nA m². has been associated with cardiomegaly, an abnormal enlargement of the fetal heart. What would the magnetic field measured by the SQUID have to be for the fetal heart to be considered abnormally large? (Enter the magnitude in pT.)
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Author:Raymond A. Serway, Chris Vuille
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Transcribed Image Text:An electrocardiogram (ECG) measures electric activity of neurons in the brain. Electroencephalograms and electromyograms respectively measure similar activity over the scalp and over the skin
surrounding muscle cells. Because the electrical activity of the human body varies with time, the time-varying electric fields in the body lead to the generation of magnetic fields that can then be
measured. The magnetocardiogram, developed in the 1960s, was the first such device. More recently, superconducting quantum interference devices (SQUIDS) have been used for these
measurements. One important application of this technique is the monitoring of the fetal heart by measuring the magnetic field produced by currents in the heart at the surface of the mother's
abdomen. The fetal heart at 28 weeks gestation can be modeled as a single-loop coil 1.50 cm in diameter, oriented so that the plane of the loop is parallel to the abdominal surface of the mother, and
a magnetic field of 10.0 pT is typically measured by the SQUID.
(a) If the distance from the abdominal wall of the mother to the fetal heart is 4.92 cm, what is the magnitude of the current in the heart (in µA) that can produce the measured magnetic field?
Assume that the measurement is made directly above and along the axis of the coil representing the fetal heart.
261.6
X
What is the fetal heart modeled as? Can any of the equations derived in the text be used to compute the magnetic field of the fetal heart? µA
(b) What is the magnetic dipole moment of the fetal heart? (Enter the magnitude in nA · m².)
nA .m²
2
(c) A magnetic dipole moment of magnitude greater than 15.0 nA · m². has been associated with cardiomegaly, an abnormal enlargement of the fetal heart. What would the magnetic field
measured by the SQUID have to be for the fetal heart to be considered abnormally large? (Enter the magnitude in pT.)
pT
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