 # The two circuits in the figure interact through small concentric circular loops of radius R and r (r<1 and R2 respectively. Inductances of the circuits are only due to circular loops. Direction of current are shown in the fig.Given : R=1cm., r=1mm , pi2=10. u0/4(pi) = 10-7N/A2 , , R1 10 ohm  R2 =1000 ohm  , e0 = 500V1. The Kirchoff's loop equn for both primary and secondary circuit is given by...2. Because R2 is very large in comparision with other circuit parameters so di2/dt can be negleted. Find i1(t) for given approximation. Use i1(0)=03. After a long time current in the primary coil i1=50 Amp and in the secondary coil i2=0.005 A.At this instant what is the magnetic energy stored in the coil system.... ROSHAN MUJEEB
askIITians Faculty 829 Points
2 years ago
Magnetic field at centre due to smaller loop
B1=μ04π.2πi1r1.......(i)B1=μ04π.2πi1r1.......(i)
Due to Bigger loopB2=μ04π.2πi2r2.......(i)B2=μ04π.2πi2r2.......(i)So net magnetic field at centreB=B1−B2=μ04π×2π(i1r1−i2r2)B=B1-B2=μ04π×2π(i1r1-i2r2)
According to questionB=12×B1B=12×B1
μ02π.2π(i1r1−i2r2)=12×μ04π.2πi1r1μ02π.2π(i1r1-i2r2)=12×μ04π.2πi1r1
i1r1−i2r2=i12r1⇒i12r1=i2r2⇒i2r2=1{r2=2r1}