8. A solenoid made of 80 loops of wire with cross-sectional area of .33 m2, a le

Question

8. A solenoid made of 80 loops of wire with cross-sectional area of .33 m2, a length of 2.5 cm, and a resistance of 4.6 is laying flat in a magnetic field of .55 T that is out of the page. Over a certain amount of time, the cross-sectional area is squished to .06 m2 and the magnetic field is turned up to 1.4 T. During this time, the induced current is .7 A. a. How long was this time? [2.4 s]

b. Mark and label both of these: the direction of the induced magnetic field, and the direction of the induced current.

Explanation / Answer

part a:

emf induced=rate of change of magnetic flux=change in magnetic flux linkage/time duration

initial flux linkage=magnetic field density*number of loops*cross sectional area

=0.55*80*0.33=14.52 Wb

final flux linkage=1.4*80*0.06=6.72 Wb

then emf induced=(14.52-6.72)/time duration

==>current induced*resistance=7.8/time

==>time=7.8/(0.7*4.6)

=2.4224 seconds

part b:

as per lenz's law, direction of induced field be such that it will oppose the field that is causing it.

as here magnetic flux is decreasing in the direction of out of page, induced magnetic flux will be along out of page.

so induced current will be in anticlockwise direction.

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