Changing Capacitance Yields a Current
Part A = I = ((K-1) * r2 * ε0 * V) / (d * Δt)
Express your answer in terms of any or all of the given variables V, K, r, d, Δt, and ε0, the permittivity of free space.
Start with the formula for capacitance:
C = ε0 * A / d
A is just the area of each of the capacitor plates and d is the distance between plates. Since the problem gives you side lengths of “r”, area is just r2. Now, to find the current, just find the change in charge over the change in time (that’s the definition of current). The charge q, is just equal to capacitance times voltage:
Q = CV
Q = (ε0 * A / d) * V.
The dielectric constant is just relative to vaccum – just subtract one from it and multiply to get the charge in different mediums. And make sure to do change in charge over change in time to get the current:
I = ((K-1) * r2 * ε0 * V) / (d * Δt)