Answer Happy

A current 𝐼(𝑡)=𝐼0cos(𝜔𝑡)I⁡(t)=I0⁢cos⁡(ω⁢t) flows
through a long solenoid with 𝑛 turns per meter and
diameter d, where 𝐼0 is the current amplitude
and 𝜔 is the angular frequency.
Derive an expression for the magnitude of the induced electric
field 𝐸in(𝑟,𝑡) inside the solenoid as a function of the
distance 𝑟 from the solenoid's central axis and the
time 𝑡. Your expression may include the
variables 𝐼0, 𝜔, 𝑑, 𝑛, and the permeability of
free space 𝜇0.
Derive an expression for the magnitude of the induced electric
field 𝐸out(𝑟,𝑡) outside the solenoid as a function
of 𝑟 and 𝑡. Your expression may include the
variables 𝐼0, 𝜔, 𝑑, 𝑛, and 𝜇0.