If it attractive it has opposite pole and if it repulsive it has same pole
Answer:
(a) 1.58 V
(b) 0.0126 Wb
(c) 0.0493 V
Solution:
As per the question:
No. of turns in the coil, N = 400 turns
Self Inductance of the coil, L = 7.50 mH =
Current in the coil, i =
A
where
![i_{max} = 1680\ mA = 1.680\ A](https://tex.z-dn.net/?f=i_%7Bmax%7D%20%3D%201680%5C%20mA%20%3D%201.680%5C%20A)
Now,
(a) To calculate the maximum emf:
We know that maximum emf induced in the coil is given by:
![e = \frac{Ldi}{dt}](https://tex.z-dn.net/?f=e%20%3D%20%5Cfrac%7BLdi%7D%7Bdt%7D)
![e = L\frac{d}{dt}(1680)cos[\frac{\pi t}{0.0250}]](https://tex.z-dn.net/?f=e%20%3D%20L%5Cfrac%7Bd%7D%7Bdt%7D%281680%29cos%5B%5Cfrac%7B%5Cpi%20t%7D%7B0.0250%7D%5D)
![e = - 7.50\times 10^{- 3}\times \frac{\pi}{0.0250}\times \frac{d}{dt}(1680)sin[\frac{\pi t}{0.0250}]](https://tex.z-dn.net/?f=e%20%3D%20-%207.50%5Ctimes%2010%5E%7B-%203%7D%5Ctimes%20%5Cfrac%7B%5Cpi%7D%7B0.0250%7D%5Ctimes%20%5Cfrac%7Bd%7D%7Bdt%7D%281680%29sin%5B%5Cfrac%7B%5Cpi%20t%7D%7B0.0250%7D%5D)
For maximum emf,
should be maximum, i.e., 1
Now, the magnitude of the maximum emf is given by:
![|e| = 7.50\times 10^{- 3}\times 1680\times 10^{- 3}\times \frac{\pi}{0.0250} = 1.58\ V](https://tex.z-dn.net/?f=%7Ce%7C%20%3D%207.50%5Ctimes%2010%5E%7B-%203%7D%5Ctimes%201680%5Ctimes%2010%5E%7B-%203%7D%5Ctimes%20%5Cfrac%7B%5Cpi%7D%7B0.0250%7D%20%3D%201.58%5C%20V)
(b) To calculate the maximum average flux,we know that:
![\phi_{m, avg} = L\times i_{max} = 7.50\times 10^{- 3}\times 1.680 = 0.0126\ Wb](https://tex.z-dn.net/?f=%5Cphi_%7Bm%2C%20avg%7D%20%3D%20L%5Ctimes%20i_%7Bmax%7D%20%3D%207.50%5Ctimes%2010%5E%7B-%203%7D%5Ctimes%201.680%20%3D%200.0126%5C%20Wb)
(c) To calculate the magnitude of the induced emf at t = 0.0180 s:
![e = e_{o}sin{\pi t}{0.0250}](https://tex.z-dn.net/?f=e%20%3D%20e_%7Bo%7Dsin%7B%5Cpi%20t%7D%7B0.0250%7D)
![e = 7.50\times 10^{- 3}\times sin{\pi \times 0.0180}{0.0250} = 2.96\times 10^{- 4} =0.0493\ V](https://tex.z-dn.net/?f=e%20%3D%207.50%5Ctimes%2010%5E%7B-%203%7D%5Ctimes%20sin%7B%5Cpi%20%5Ctimes%200.0180%7D%7B0.0250%7D%20%3D%202.96%5Ctimes%2010%5E%7B-%204%7D%20%3D0.0493%5C%20V)
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