\' Course Contents» » Set 6 » Calculate the emf In the loop ?53 function of time
ID: 2035997 • Letter: #
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' Course Contents» » Set 6 » Calculate the emf In the loop ?53 function of time 31p4) The magnetic feld through ? single loop of wire 12.0 cm an radius and of 8.5 ? resistance charges with time as shown in the figure. Calculate the emf 'n the loop as a function of time. 1.0 Eo5 0.5 0 20 4.0 6.0 8.0 t (s) What is the emf at t-1.0 s? For the sign take the loop in the plane of the paper, and the magnetic field out of the paper. Take lockwise to be positive emf. Submit Answer Tries o/99 What is the emf at t-3.0s? Submit Anewer Tries 0/99 What is the emf at t-50s ubmit Answer Tries 0/99 What is the current at t-1.0Explanation / Answer
Given,
r = 12 cm = 0.12 m ; R = 8.5 Ohm ;
A = pi r^2 = 3.14 x 0.12^2 = 0.045
a)We know that the induced emf is given by:
emf = d(phi)/dt = d(BA)/dt = A dB/dt
for t = 1 s ; B = 0.25 T
emf = 0.045 x 0.25/1 = 0.011 V
Hence, emf = 0.011 V = 11 mV
b)for t = 3 s ; B = 0.5 T
emf = 0.045 x 0.5/3 = 0.0075 V
Hence, emf = 0.0075 V = 7.5 mV
c)for t = 5 sec ; B = 0.25 T
emf = 0.045 x 0.25/5 = 0.0023 V
Hence, emf = 0.0023 V = 2.3 mV
d)for t = 1 s ; B = 0.25 ; emf = 0.011 V (part a)
from Ohm's law, V = IR=> I = V/R = 0.011/8.5 = 0.0013 A
Hence, I = 0.0013 A = 1.3 mA
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