A) We need to calculate the Magnetic flux of a Solenoid,
[tex]\Phi = BA[/tex]
Where B is the magnetic field and A the Area.
[tex]B=\frac{\mu_0 N_2 I}{l}[/tex]
Here \mu_0 is the permeability constant, I the current and N number of turns.
Replacing we have,
[tex]\Phi = \frac{\mu_0 N_2 I}{l}(\pi r^2)[/tex]
[tex]\Phi = \frac{(4\pi*10^{-7})(350)(0.12)}{25*10^{-2}} (\pi*\frac{2.5*10^{-2}}{2}^2)[/tex]
[tex]\Phi = 1.036*10^{-7}Wb[/tex]
B) We calculate the mutual inductance, so
[tex]M=\frac{N_1 \Phi}{i}[/tex]
[tex]M=\frac{21*1.036*10^{-7}}{0.12}[/tex]
[tex]M=1.813*10^{-5}H[/tex]
c) We calculate the emf
[tex]\epsilon = -M \frac{dI}{dt}[/tex]
[tex]\epsilon = -1.813*10^{-5}*1700[/tex]
[tex]\epsilon= -0.030V[/tex]
