Changing Capacitance Yields a Current

Part A = I = ((K-1) * r^{2} * ε_{0} * V) / (d * Δt)

**Solution Below:**

Part A

Express your answer in terms of any or all of the given variables V, K, r, d, Δt, and ε

_{0}, the permittivity of free space.

Start with the formula for capacitance:

C = ε_{0} * 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 r^{2}. 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 = (ε_{0} * 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) * r^{2} * ε_{0} * V) / (d * Δt)