Question

To monitor the breathing of a hospital patient, a thin belt isgirded around the patient's chest. The belt is a200-turn coil. When the patient inhales,

Other
ANSWERED
asked 2021-04-23
To monitor the breathing of a hospital patient, a thin belt isgirded around the patient's chest. The belt is a200-turn coil. When the patient inhales, the area encircled by the coil increases by \(\displaystyle{39.0}{c}{m}^{{2}}\). The magnitude of the Earth's magnetic field is 50.0uT and makes an angle of 28.0 degree with the plane of the coil. Assuming a patien takes 1.80s toin hale, find the magnitude of the average induced emf in the coilduring that time.
Do I use the equation \(\displaystyle{E}={N}\cdot{A}\cdot{B}{w}{\sin{{w}}}{t}\)?

Answers (1)

2021-04-25
You were close. This is Faraday's Law of Induction.
The flux is \(\displaystyle\phi={N}{B}{A}{\cos{\theta}}\)
N is the number of turns
B is the strength of the magnetic field (should be in T)
A is the area of the loop (should be in \(\displaystyle{m}^{{2}}\))
The angle is between the magnetic field and the normal(perpendicular to the coil) so it would be cos(90.0 - 28.0).
The EMF = - rate of change in flux, or
\(\displaystyle{E}{M}{F}={\frac{{-\triangle\phi}}{{\triangle{t}}}}\)
The \(\displaystyle\triangle\phi={N}{B}{\left(\triangle{A}\right)}{\cos{\theta}}\) (since A is the only thingthat changes, and you don't need the original A, only the change in A)
\(\displaystyle\triangle={1.80}{s}\)
If the above still confuses you...
Flux Linkage, or simply flux, refers to the magnetic field linespassing through the area of a loop:
image
The diagram on the left shows the loop allows the magnetic fieldvectors to pass through it (\(\displaystyle\theta\) ˜ 0 deg), but on the right,the magnetic field vectors cannot pass through it (\(\displaystyle\theta\) = 90deg).
The flux is \(\displaystyle\phi={N}{B}{A}{\cos{\theta}}\), so in the case on the cos (0deg) = 1, so \(\displaystyle\phi={N}{B}{A}\), but on the right cos (90 deg) = 0, so \(\displaystyle\phi={0}\).
The way that \(\displaystyle\theta\) is defined is it is perpendicular to the planeof the loops. Think about how the diagram on the right has a \(\displaystyle\theta\)= 90 deg. The area vector is pointing straight out at us in theright figure.
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-02-17
A square loop of copper wire is initially placed perpendiclar to the lines of a constant magnetic field of \(\displaystyle{5}\times{10}^{{3}}\) T.The area enclosed by the loop is 0.2 square meter. the loopis then turned through an angle \(\displaystyle{90}^{\circ}\) so thatthe plane of the loop is parallel to the field lines. the turntakes 0.1 second. what is the average emf induced in the loop during the turn?
asked 2020-12-17

17. A planar coil of wire has a single turn. Thenormal to this coil is parallel to a uniform and constant (in time)magnetic field of 1.7 T. An emf that has a magnitude of 2.6 Vis induced in this coil because the coil's area A isshrinking. What is the magnitude of ? A/? t, whichis the rate (in \(m^2/s\)) at which the area changes?

asked 2021-03-30
A long, straight, copper wire with a circular cross-sectional area of \(\displaystyle{2.1}{m}{m}^{{2}}\) carries a current of 16 A. The resistivity of the material is \(\displaystyle{2.0}\times{10}^{{-{8}}}\) Om.
a) What is the uniform electric field in the material?
b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?
c) What is the displacement current density in the material in part (b)?
d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?
asked 2021-02-19
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
...