i cant understand how they how the member of which i point too
You haven't designated the two inductors, so I'm going to call the inductor which is common to the two loops L1, and the other inductor L2.
The term you're asking about comes about because the current I2 passes through L2 and induces a voltage in L1. The voltage induced in L1 has the value I2*M.
I think you may have made a mistake in calculating M. It looks like you didn't properly take into account the coefficient of coupling which is .8. Shouldn't M be j40 instead of j50?
L1 is 0.02
L2 is 0.005
is there still a mistake?
M = .8 * SQRT(.02*.005) = .8 * .01 = .008
then its impedance would be 40j, not 50j.
so if k=0.8 than we need to add 0.8 I2
this is the affect of the other coil
they say jwM=j*5000*0.01=50
Look at the computation you have in your image:
0.8 = K = |M|/SQRT(L1*L2) => |M| = .8*SQRT(L1*L2). (What happened to the .8?)
From that M = .008
You should be able to find K = M/SQRT(L1*L2) in any textbook, or here:
Perhaps "they" have made a mistake; it does happen.
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