# Solenoid and induced electric fields

Let us suppose there is a solenoid which has $$n$$ turns per unit length the current is varying with time as $$I =kt$$ where k is a constant if the current is flowing then there must be induced electric field inside and outside the solenoid since $$\oint E_{induced}.dl= -\frac{d\phi}{dt}$$. now my question is if I place a small charge anywhere inside or outside the solenoid will it move with the induced electric field in a circle? The induced electric field is in blue.please ignore the current equation in the figure.