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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 field is in blue color. Please ignore the current equation in the image. The induced electric field is in blue.please ignore the current equation in the figure.

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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.

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  • $\begingroup$ 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? $\endgroup$ – shahroze shahab Jul 1 at 21:35
  • $\begingroup$ 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. $\endgroup$ – Puk Jul 1 at 21:41
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Yes, this is exactly what causes inductive coupling.

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  • $\begingroup$ So the charge will accelerate and move in the circular path or will it move with a constant velocity? $\endgroup$ – shahroze shahab Jul 1 at 21:05
  • $\begingroup$ Please consider elabprating and explaining your answer. $\endgroup$ – user258881 Jul 2 at 4:59

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