In the figure, a rectangular loop of wire with length a = 3.0 cm, width b = 0.98
ID: 1782198 • Letter: I
Question
In the figure, a rectangular loop of wire with length a = 3.0 cm, width b = 0.98 cm, and resistance R = 0.70 m is placed near an infinitely long wire carrying current i = 4.7 A. The loop is then moved away from the wire at a constant speed v = 4.7 mm/s. When the center of the loop is at distance r = 2.1 cm, what are (a) the magnitude of the magnetic flux through the loop and (b) the current in amperes induced in the loop?
(a) Number Units This answer has no units° (degrees)mkgsm/sm/s^2JVmAnWbN/m^2 or Pakg/m^3Explanation / Answer
when center is at r = 2.1 cm
magnetic field due to wire
B = Uo*i/(2*pi*r) = 4*pi*10^-7*4.7/(2*pi*0.021) = 447.61*10^-7 T
=> magnetic flux through the loop
flux = BA = 447.61*10^-7*0.03*0.0098 = 13.15*10^-9 Wb part (a)
induce emf , E =vBL = 4.7*10^-3*447.61*10^-7*0.03 =63.11*10^-10 volt
current induce , i = E/R = 63.11*10^-10 / (0.70*10^-3) = 90.15*10^-7 A
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