During transcranial magnetic stimulation (TMS) treatment, a magnetic field typically of magnitude 0.50 T is produced in the brain using external coils. During the treatment, the current in the coils (and hence the magnetic field in the brain) rises from zero to its peak in about 75 us. Assume that the magnetic field is uniform over a circular area of diameter 1.7 cm inside the brain. What is the magnitude of the average induced emf |E| around this area in the brain during the treatment? |E| = V

During transcranial magnetic stimulation (TMS) treatment, a magnetic field typically of magnitude 0.50 T is produced in the brain using external coils. During the treatment, the current in the coils (and hence the magnetic field in the brain) rises from zero to its peak in about 75 us. Assume that the magnetic field is uniform over a circular area of diameter 1.7 cm inside the brain. What is the magnitude of the average induced emf |E| around this area in the brain during the treatment? |E| = V

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter23: Faraday’s Law And Inductance

Section: Chapter Questions

Problem 4OQ: A circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.060 T....

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A circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.060 T. The plane of the loop is perpendicular to the direction of the magnetic field. In a time interval of 0.50 s, the magnetic field changes to the opposite direction with a magnitude of 0.040 T. What is the magnitude of the average emf induced in the loop? (a) 0.20 V (b) 0.025 V (c) 5.0 mV (d) 1.0 mV (e) 0.20 mV
A rectangular conducting loop with dimensions w = 32.0 cm and h = 78.0 cm is placed a distance a = 5.00 cm from a long, straight wire carrying current I = 7.00 A in the downward direction (Fig. P32.75). a. What is the magnitude of the magnetic flux through the loop? b. If the current in the wire is increased linearly from 7.00 A to 15.0 A in 0.230 s, what is the magnitude of the induced emf in the loop? c. What is the direction of the current that is induced in the loop during this time interval?
A conducting single-turn circular loop with a total resistance of 5.00 is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by B = a + bt2 ct3, where a = 4.00 Wb, b = 11.0 Wb/s2, and c = 6.00 Wb/s3. B is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 3.50 s?
A thin conducting bar (60.0 cm long) aligned in the positive y direction is moving with velocity v=(1.25m/s)i in a region with a spatially uniform 0.400-T magnetic field directed at an angle of 36.0 above the xy plane. a. What is the magnitude of the emf induced along the length of the moving bar? b. Which end of the bar is positively charged?
A metal bar of length 25 cm is placed perpendicular to a uniform magnetic field of strength 3 T. (a) Determine the induced emf between the ends of the rod when it is not moving, (b) Determine the emf when the rod is moving perpendicular to its Length and magnetic field with a speed of 50 cm/s.
The magnetic flux through a metal ring varies with time t according to (B = at3 bt2, where (B is in webers, a = 6.00 s3, b = 18.0 s2, and t is in seconds. The resistance of the ring is 3.00 . For the interval from t = 0 to t = 2.00 s, determine the maximum current induced in the ring.
A 5000-pF capacitor is charged to 100 V and then quickly connected to an 80-mH inductor. Determine (a) the maximum energy stored in the magnetic field of the inductor, (b) the peak value of the current, and (c) the frequency of oscillation of the circuit.
Design a current loop that, when rotated in a uniform magnetic field of strength 0.10 T, will produce an emf =0 sin t. where 0=110V and 0=110V .
A parallel-plate capacitor with plate separation d is connected to a source of emf that places a time-dependent voltage V(t) across its circular plates of radius r0and area (a) Write an expression for the time rate of change of energy inside the capacitor in terms of V(t) and dV(t)/ dt. (b) Assuming that V(t) is increasing with time, identify the directions of the elecuic field lines inside the capacitor and of the magnetic field lines at the edge of the region between the plates, and then the direction of the Poynting vector S at this location. (c) Obtain expressions for the time dependence of E(t), for B(t) from the displacement current, and for the magnitude of the Poynting vector at the edge of the region between the plates. (d) From S , obtain an expression In terms of ‘(t) and dV(t)/dt for the rate at which electromagnetic field energy the region between the plates. (e) Compare the results of pails (a) and (d) and explain the relationship between them.
To monitor the breathing of a hospital patient, a thin belt is girded around the patients chest as in Figure P20.21. The belt is a 200-turn coil. When the patient inhales, the area encircled by the coil increases by 39.0 cm2. The magnitude of Earths magnetic field is 50.0 T and makes an angle of 28.0 with the plane of the coil. Assuming a patient takes 1.80 s to inhale, find the magnitude of the average induced emf in the coil during that time. Figure P20.21
A 50-turn coil has a diameter of 15 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.50 T so that the face of the coil and the magnetic field are perpendicular. Find the magnitude of the emf induced in the coil if the magnetic field is reduced to zero uniformly in (a) 0.10 s, (b) 1.0 s, and (c) 60 s.