In a long staright solenoid with cross-sectional radius `a` and number of turns per unit length `n` a current varies with a constant velocity` dotI A//s`. Find the magntidue of the eddy current field strength as a function of the distance `r` from the solenoid axis. Draw the appoximate plot of this function.

Explanation

We use `B = mu_(0) n I`
Then, from the law of electromagnetic induction
`oint vec(E).d. vec(l) = (d Phi)/(dt)`
So, for `r lt a`
`E_(0) 2pi r = -pi r^(2) mu_(0) n dotI` or`E_(varphi) = - (1)/(2) mu_(0) n r dotI`. (where `I = dI//dt`)
For `r gt a`
`E_(varphi) 2pi r = -pi a^(2) mu_(0) n dotI`, or `E_(varphi) = -mu_(0) n dotI a^(2) //2r`
The meaning of minus sign can be deduced from Lenz'z law.