While solving some electromagnetic induction questions, I stumbled upon one that kept a solenoid in a loop with common axis. We were asked to find the current in the loop when a current (and thus the ensuing magnetic field) in the solenoid changes.
Now we only consider field inside the solenoid. So taking a similar case, suppose we keep a loop in perfect vacuum and pass a time-varying magnetic field perpendicular to its plane such that the field is only nonzero for some smaller area within the loop (and zero on the loop itself).
Will a current be induced?
If yes, how does the information about flux change reaches the loop and what carries that effect? For example, spacetime carries the effect of a mass being present near another i.e. gravity and magnetic fields carry effects of two magnets coming close i.e. repulsion or attraction. Nothing like this seems to exist between the field and the loop so what carries the effect of the field changing, to induce a current in the loop?
- $\begingroup$It seems to me you are asking about the induced electric field - outside the solenooid and in the space where both the magnetic field and the magnetic induction are zero. Correct? Are you interested in the quasi-static situation (where this 'mediator' field is estabilished and changes instantaneously and without propagation) or in the actual dynamic case where you would see this field propagate at the speed of light from the solenoid?$\endgroup$Peltio– Peltio2025-11-03 21:52:02 +00:00CommentedNov 3 at 21:52
- $\begingroup$Thanks for going through my query , I think my statement relates more to the quasi-static case , but I'd like to understand what differences show up when we take the dynamic case .$\endgroup$gm1210– gm12102025-11-04 04:15:23 +00:00CommentedNov 4 at 4:15
- $\begingroup$I totally acknowledge any closures ; but I request any member putting it to please leave details about the reason for closure in the comments , It will really help me understand my mistake and improve it better , for I am new to this community . Thanks .$\endgroup$gm1210– gm12102025-11-04 09:56:08 +00:00CommentedNov 4 at 9:56
- $\begingroup$@gm1210 Why wouldn't a current be induced? Faraday's law only requires the rate of change of magnetic flux through the loop, not the magnetic field at a particular point.$\endgroup$Vincent Thacker– Vincent Thacker2025-11-04 11:57:23 +00:00CommentedNov 4 at 11:57
- $\begingroup$Yes that is clear , but is there some way we can define how it happened . Like there is always some kind of field linking the cause and effect points in such phenomenon , but here there is non . I don't know if we have an explanation , but another interesting question can be - What if here , it wasn't a closed loop but split a some point ? I'll love to hear about this situation$\endgroup$gm1210– gm12102025-11-04 13:26:43 +00:00CommentedNov 4 at 13:26
1 Answer1
Yes a current will be induced in the loop circling the solenoid, in a region of space where the magnetic field B(t) and its time derivative dB(t)/dt are both zero.
How is this possible? Associated with the changing magnetic field inside the solenoid, there is an induced electric field Eind, curling around the dB/dt field lines. This field is present both inside the solenoid, both on the outside.Here is a drawing of the field lines.
It is this field that is responsible for the current in the closed (resistive) loop in the region of space where both the magnetic field B and the magnetic induction dB/dt are zero. If the conducting loop is broken, the field will cause surface charge to accumulate on the surface and in particular at the extremities of the conductor, so that there will be a strong coulombian electric field in the small space between the terminals. This is the EMF linked by the loop. The surface charge will redistribute over time to give a net zero electric field inside the open loop (after all the current is zero) and a non-zero electric field in the space between the terminals.
When you close the gap with a resistor, there will be a distribution of charge at the interfaces between the conductor and the resistor so that the electric field inside both will obey Ohm's law. In particular inside the materials you will see a very small, near zero total electric field following the profile of the good conductor and a strong total electric field inside the resistor.
Note: the configuration of the total electric field in the space around the circuit is in general complex as it is the superposition of the analytically simple induced electric field (simple in the case of an infinitely long circular solenoid) and the coulombian field generated by the complex and geometry dependent distribution of surface and interface charges.
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