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Another contemporary area of research in which electromagnetic induction is being successfully implemented is transcranial magnetic stimulation (TMS) . A host of disorders, including depression and hallucinations, can be traced to irregular localized electrical activity in the brain. In transcranial magnetic stimulation, a rapidly varying and very localized magnetic field is placed close to certain sites identified in the brain. The usage of TMS as a diagnostic technique is well established.

Check out this Youtube video to see how rock-and-roll instruments like electric guitars use electromagnetic induction to get those strong beats.

Summary

  • Hard drives utilize magnetic induction to read/write information.
  • Other applications of magnetic induction can be found in graphics tablets, electric and hybrid vehicles, and in transcranial magnetic stimulation.

Key equations

Magnetic flux Φ m = S B · n ^ d A
Faraday’s law ε = N d Φ m d t
Motionally induced emf ε = B l v
Motional emf around a circuit ε = E · d l = d Φ m d t
Emf produced by an electric generator ε = N B A ω sin ( ω t )

Additional problems

Shown in the following figure is a long, straight wire and a single-turn rectangular loop, both of which lie in the plane of the page. The wire is parallel to the long sides of the loop and is 0.50 m away from the closer side. At an instant when the emf induced in the loop is 2.0 V, what is the time rate of change of the current in the wire?

Figure shows a long, straight wire and a single-turn rectangular wire loop with length 3.0 m and width 0.5cm, both of which lie in the plane of the page. The wire is parallel to the long sides of the loop and is 0.50 m away from the closer side.

3.0 A/s

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A metal bar of mass 500 g slides outward at a constant speed of 1.5 cm/s over two parallel rails separated by a distance of 30 cm which are part of a U-shaped conductor. There is a uniform magnetic field of magnitude 2 T pointing out of the page over the entire area. The railings and metal bar have an equivalent resistance of 150 Ω. (a) Determine the induced current, both magnitude and direction. (b) Find the direction of the induced current if the magnetic field is pointing into the page. (c) Find the direction of the induced current if the magnetic field is pointed into the page and the bar moves inwards.

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A current is induced in a circular loop of radius 1.5 cm between two poles of a horseshoe electromagnet when the current in the electromagnet is varied. The magnetic field in the area of the loop is perpendicular to the area and has a uniform magnitude. If the rate of change of magnetic field is 10 T/s, find the magnitude and direction of the induced current if resistance of the loop is 25 Ω .

2.83 × 10 −4 A , the direction as follows for increasing magnetic field:
Figure shows a circular loop placed between two poles of a horseshoe electromagnet.

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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.

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A coil with 50 turns and area 10 cm 2 is oriented with its plane perpendicular to a 0.75-T magnetic field. If the coil is flipped over (rotated through 180 ° ) in 0.20 s, what is the average emf induced in it?

0.375 V

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A 2-turn planer loop of flexible wire is placed inside a long solenoid of n turns per meter that carries a constant current I 0 . The area A of the loop is changed by pulling on its sides while ensuring that the plane of the loop always remains perpendicular to the axis of the solenoid. If n = 500 turns per meter, I 0 = 20 A, and A = 20 cm 2 , what is the emf induced in the loop when d A / d t = 100 ?

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Questions & Answers

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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