A 0.210–A current is charging a capacitor that has circular plates 11.6 cm in radius. The plate separation is 4.00 mm.(a) What is the time rate of increase of electric field between the plates? V/(m·s)(b) What is the magnetic field between the plates 5.00 cm from the center?

(a) The time rate of increase of electric field between the plates can be calculated using the formula for the current through a capacitor, which is I = ε0 * A * (dE/dt), where I is the current, ε0 is the permittivity of free space, A is the area of the capacitor, and dE/dt is the rate of change of the electric field.

First, we need to calculate the area of the capacitor. The area of a circle is given by the formula A = πr^2, where r is the radius. In this case, the radius is 11.6 cm, or 0.116 m. So, A = π * (0.116 m)^2 = 0.0424 m^2.

Next, we can rearrange the formula for the current through a capacitor to solve for dE/dt: dE/dt = I / (ε0 * A). The permittivity of free space ε0 is approximately 8.85 * 10^-12 C^2/N*m^2.

So, dE/dt = 0.210 A / (8.85 * 10^-12 C^2/N*m^2 * 0.0424 m^2) = 5.6 * 10^12 V/(m·s).

(b) The magnetic field between the plates can be calculated using Ampere's law, which states that the magnetic field around a current-carrying wire is given by B = μ0 * I / (2 * π * r), where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

In this case, the "wire" is the edge of the capacitor, and the distance r is 5.00 cm, or 0.050 m. The permeability of free space μ0 is approximately 4π * 10^-7 T*m/A.

So, B = 4π * 10^-7 T*m/A * 0.210 A / (2 * π * 0.050 m) = 2.64 * 10^-8 T.