Magnetic resonance imaging (MRI) is a common non-invasive medical imaging method with high resolution and soft tissue contrast. The main component of an MRI scanner is a very strong superconducting magnet with the magnetic field strength measured in Teslas (T). The magnet resembles a large pipe, 1.25 m long, open on both ends, with a bore diameter of 0.6 m.The magnetic field is generated by an electric current flowing in coils of superconducting wire. The superconductor is cooled to 4 K with liquid helium and has zero electrical resistance. Liquid helium that boils out of the MRI scanner is stored in a collection system, cooled back into a liquid, and returned to the MRI scanner.During imaging, the MRI scanner generates rapid magnetic field oscillations that cause vibrations and loud sounds. Researchers measured the sounds of MRI at different magnetic field strengths and compared them to common noise sources. Table 1 lists the sound intensity in decibels (dB) and predominant frequency for these sounds.Table 1 Sound Intensity and Predominant Frequency from Different Noise SourcesThe noise frequencies were determined using frequency selective RC circuits with a resistor R and capacitor C in series. Sounds with frequencies above the cutoff frequency fc of the circuit were suppressed. The value of fc in Hz was calculated with Equation 1.fc=12πRC𝑓c=12𝜋RCEquation 1MRI can be combined with another imaging method, positron emission tomography (PET), to detect cancer. PET imaging maps the uptake of a radioactive metabolite. The radioactive decay emits a positron that annihilates with an electron and forms gamma rays that are imaged by the scanner. Question 49How will the work done by the Lorentz force on an electron traveling through the magnetic field of an MRI scanner change if the magnetic field strength is increased?A.The work will not change, because it is always zero.B.The work will increase, because the velocity of the electron will increase.C.The work will increase, because the force on the electron will increase.D.The work will decrease, because the velocity of the electron will decrease.
Question
Magnetic resonance imaging (MRI) is a common non-invasive medical imaging method with high resolution and soft tissue contrast. The main component of an MRI scanner is a very strong superconducting magnet with the magnetic field strength measured in Teslas (T). The magnet resembles a large pipe, 1.25 m long, open on both ends, with a bore diameter of 0.6 m.The magnetic field is generated by an electric current flowing in coils of superconducting wire. The superconductor is cooled to 4 K with liquid helium and has zero electrical resistance. Liquid helium that boils out of the MRI scanner is stored in a collection system, cooled back into a liquid, and returned to the MRI scanner.During imaging, the MRI scanner generates rapid magnetic field oscillations that cause vibrations and loud sounds. Researchers measured the sounds of MRI at different magnetic field strengths and compared them to common noise sources. Table 1 lists the sound intensity in decibels (dB) and predominant frequency for these sounds.Table 1 Sound Intensity and Predominant Frequency from Different Noise SourcesThe noise frequencies were determined using frequency selective RC circuits with a resistor R and capacitor C in series. Sounds with frequencies above the cutoff frequency fc of the circuit were suppressed. The value of fc in Hz was calculated with Equation 1.fc=12πRC𝑓c=12𝜋RCEquation 1MRI can be combined with another imaging method, positron emission tomography (PET), to detect cancer. PET imaging maps the uptake of a radioactive metabolite. The radioactive decay emits a positron that annihilates with an electron and forms gamma rays that are imaged by the scanner. Question 49How will the work done by the Lorentz force on an electron traveling through the magnetic field of an MRI scanner change if the magnetic field strength is increased?A.The work will not change, because it is always zero.B.The work will increase, because the velocity of the electron will increase.C.The work will increase, because the force on the electron will increase.D.The work will decrease, because the velocity of the electron will decrease.
Solution
The work done by the Lorentz force on an electron traveling through the magnetic field of an MRI scanner will increase if the magnetic field strength is increased. This is because the Lorentz force is directly proportional to the magnetic field strength. Therefore, the correct answer is C. The work will increase, because the force on the electron will increase.
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