Answer
a. $2.88\times10^{-7}H$.
b. $ 1.42\times10^{-5}V$.
Work Step by Step
See Example 30.1, which gives the mutual inductance for these 2 solenoids. Let “1” be the outer solenoid.
a.
$$M=\frac{\mu_0 A N_1N_2}{l}$$
$$M=\frac{(4\pi \times10^{-7}Wb/m \cdot A)\pi(6.00\times10^{-4}m)^2(6750)(15)}{0.500m}$$
$$=2.88\times10^{-7}H $$
b. $|\epsilon_2|=M|\frac{di_1}{dt}|=(2.88\times10^{-7}H)(49.2A/s)=1.42\times10^{-5}V$.
