# 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.

Yes, the charge will move under the influence of the induced E-field, but it will not move in a circle: this would require a centripetal force, but there is none. Instead, the (positive) charge will start to move in the direction of the E-field, then spiral outward.

• So what causes the charges to move in a circle if a ring of charge is placed in with its axis coinciding with the solenoid? What gives the necessary centripetal force in this case? Commented Jul 1, 2020 at 21:35
• If the ring is solid, it needs to be held together somehow. The stress within the ring is what provides the centripetal force in that case.
– Puk
Commented Jul 1, 2020 at 21:41

Yes, this is exactly what causes inductive coupling.

• So the charge will accelerate and move in the circular path or will it move with a constant velocity? Commented Jul 1, 2020 at 21:05