In the operating room, anesthesiologists use mass spectrometers to monitor the respiratory gases of patients undergoing surgery. One gas that is often monitored is the anesthetic isoflurane (molecular mass = 3.06 10-25 kg). In a spectrometer, a singly ionized molecule of isoflurane (charge = +e) moves at a speed of 4.20 103 m/s on a circular path that has a radius of 0.035 m. What is the magnitude of the magnetic field that the spectrometer uses?
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To calculate the magnitude of the magnetic field (B) that the spectrometer uses, you can use the equation for the magnetic force (F) acting on a charged particle moving in a magnetic field:
F = q * v * B
In this equation:
- q is the charge of the particle
- v is the speed of the particle
- B is the magnetic field
- F is the magnetic force
In this case, the charged particle is the singly ionized molecule of isoflurane, which has a charge of +e (where e is the elementary charge).
Since the particle moves in a circular path, there is a relationship between the magnetic force and the centripetal force (F_c) acting on the particle:
F_c = (m * v^2) / r
In this equation:
- m is the mass of the particle
- v is the speed of the particle
- r is the radius of the circular path
Since you know the speed of the particle and the radius of the circular path, you can calculate the centripetal force.
Now, you need to equate the magnetic force and the centripetal force:
F_c = q * v * B
(m * v^2) / r = q * v * B
m * v / r = q * B
Now, isolate B:
B = (m * v) / (q * r)
To solve this equation, you need the values of the mass of the isoflurane molecule (m), the speed of the particle (v), the charge of the particle (q), and the radius of the circular path (r).