A single-turn circular loop of wire of radius 65 mm lies in a plane perpendicular to a spatially uniform magnetic field. During a 0.10 s time interval, the magnitude of the field increases uniformly from 350 to 650 mT. a) Determine the emf induced in the loop. (b) If the magnetic field is directed out of the page, what is the direction of the current induced in the loop?

Question

Gary Blake

Physics

24 May, 21:48

A single-turn circular loop of wire of radius 65 mm lies in a plane perpendicular to a spatially uniform magnetic field. During a 0.10 s time interval, the magnitude of the field increases uniformly from 350 to 650 mT. a) Determine the emf induced in the loop. (b) If the magnetic field is directed out of the page, what is the direction of the current induced in the loop?

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Travis Hanson · Answer 1

change in flux = no of turns x area of loop x change in magnetic field

= 1 x π 65² x 10⁻⁶ x (650 - 350) x 10⁻³

= 3.9 x 10⁻³ weber.

rate of change of flux = change of flux / time

= 3.9 x 10⁻³ /.10

= 39 x 10⁻³ V

= 39 mV.

Since the magnetic flux is directed outside page and it is increasing, induced current will be clockwise so that magnetic field is produced in opposite direction to reduce it, as per Lenz's law.