Two solenoids `A` and `B` spaced close to each other and sharing the same cylindrical axis have `400` and `700` turns, respectively. A current of `3.50A` in coil `A` produced an average flux of `300muT-m^2` through each turn of `A` and `a` flux of `90.0mT-m^2` through each turn of `B`.
a. Calculate the mutual inductance of the two solenoids.
b.What is the self inductance of `A`?
c. What emf is induced in `B` when the current in `A` increases at the rate of `0.5A//s`?

Explanation

a. `M=(N_Bphi_B)/i_A`
`=((700)(90xx10^-6))/3.5`
`=1.8xx10^-2H`
b. `L_A=(N_Aphi_A)/i_A`
`=((400)(300xx10^-6))/3.5`
`=3.43xx10^-2H`
c. `e_B=M((di_A)/(dt))`
`=(1.8xx10^-2)(0.5)`
`=9.0xx10^-3V`