Final answer:
The magnitude of the displacement current through a circular loop can be found using Faraday's Law and Ohm's Law, with an example analogous to the provided scenarios involving a solenoid with a time-dependent current.
Step-by-step explanation:
To determine the magnitude of the displacement current through a circular loop, we can use one of the provided scenarios as an analogous example. In the case of a solenoid with a time-varying current as mentioned in question 89, the magnetic flux Φ through a loop of radius r ≤ a within the solenoid will change with time, inducing an electromotive force (EMF) and thus a displacement current in the loop surrounding the solenoid. The magnitude of the magnetic flux is determined by integrating the magnetic field B over the area A of the loop, which is given by Φ = B ⋅ A. The induced EMF (ε) is then obtained through Faraday's Law, ε = -dΦ/dt, which, when divided by the resistance R of the loop, yields the magnitude of the induced current, I = ε/R. For example, according to the statement 'When divided by the resistance R of the loop, this yields for the magnitude of the induced current Br² w/2R', we can see that the magnitude of the current depends on the magnetic field B, the radius r of the loop, the angular frequency w, and the resistance R.