In the figure, a rectangular loop of wire with length a = 3.8 cm, width b = 1.3

Question

In the figure, a rectangular loop of wire with length a = 3.8 cm, width b = 1.3 cm, and resistance R = 0.82 m is placed near an infinitely long wire carrying current i = 6.8 A. The loop is then moved away from the wire at a constant speed v = 1.9 mm/s. When the center of the loop is at distance r = 2.9 cm, what are (a) the magnitude of the magnetic flux through the loop and (b) the current in amperes induced in the loop?

http://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c30/fig30_50.gif

Explanation / Answer

a =3.8 cm , b =1.3 cm , R =0.82 milliohm, i =6.8 A, v =1.9 mm/s , r =2.9 cm

uo =4pi*10^-7 T.m/A

magnetic filed B = uoi/2r

B = (4*3.14*10^-7*6.8)/(2*2.9*10^-2) =1.47*10^-4 T

(a) flux phi = BA =( uoi/2r )(ab)

= (4*3.14*10^-7*6.8*3.8*1.3*10^-4)/(2*2.9*10^-2)

flux =7.27*10^-8 T.m^2

(b) from faradays law induced emf V = BvL

from ohms law V= iR

Bvb = iR

1.47*10^-4*1.9*10^-3*1.3*10^-2 = i*0.82*10^-3

i =4.43*10^-6 A

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