Given data:
- Radius of the plates (r) = 12 cm = 0.12 m
- Distance between the plates (d) = 4 mm = 0.004 m
- Capacitance of the capacitor (C) = 100 pF = 100 × 10^(-12) F
- Conduction current (I) = 0.15 A

Calculation:

Step 1: Calculate the magnetic field at a distance r/2 from the center of the plates.

The magnetic field (B) at a distance r/2 from the center of the plates can be calculated using Ampere's law. Ampere's law states that the line integral of the magnetic field around a closed loop is equal to the product of the current enclosed by the loop and the permeability of free space (μ0).

The magnetic field due to the conduction current can be given as:
B = (μ0 * I) / (2πr)

Substituting the given values:
r = 0.12 m
I = 0.15 A
μ0 = 4π × 10^(-7) T·m/A

B = (4π × 10^(-7) T·m/A * 0.15 A) / (2π * 0.12 m)
B = 5 × 10^(-6) T

Therefore, the magnetic field at a distance r/2 from the center of the plates is 5 μT.

Step 2: Calculate the magnetic field between the plates along the axis.

The magnetic field between the plates of the capacitor can be considered as the superposition of the magnetic fields due to the conduction current and the displacement current, as the plates of a parallel plate capacitor act as a capacitor and a solenoid simultaneously.

The displacement current (Id) can be calculated using the formula:
Id = ε0 * dV/dt

Where:
ε0 is the permittivity of free space (8.85 × 10^(-12) F/m)
dV/dt is the rate of change of voltage across the plates

Since the plates are connected to a capacitor, the voltage across the plates (V) can be calculated using the formula:
V = Q / C

Where:
Q is the charge on the capacitor
C is the capacitance of the capacitor

The charge on the capacitor (Q) can be calculated using the formula:
Q = C * V

Substituting the given values:
C = 100 × 10^(-12) F
V = Q / C = (0.15 A * t) / (100 × 10^(-12) F)
V = 1.5 * 10^9 t

The rate of change of voltage (dV/dt) can be calculated as:
dV/dt = 1.5 * 10^9

The displacement current (Id) can be calculated as:
Id = ε0 * dV/dt = 8.85 × 10^(-12) F/m * 1.5 * 10^9
Id = 13.275 A

Therefore, the displacement current between the plates is 13.275 A.

The total magnetic field between the plates along the axis is the sum of