Final Answer:
The spacing between the plates is 1.00 x 10^-4 m.
Step-by-step explanation:
The surface charge density on a parallel-plate capacitor is given by the following equation:
σ = Q / A
where:
σ is the surface charge density
Q is the charge on the capacitor plates
A is the area of each capacitor plate
The charge on the capacitor plates can be calculated using the following equation:
Q = CV
where:
Q is the charge on the capacitor plates
C is the capacitance of the capacitor
V is the potential difference between the capacitor plates
The capacitance of a parallel-plate capacitor is given by the following equation:
C = ε₀A / d
where:
C is the capacitance of the capacitor
ε₀ is the permittivity of free space
A is the area of each capacitor plate
d is the spacing between the capacitor plates
Plugging in the values we know, we can get the following equation:
σ = (ε₀AV) / (d²)
Solving for d, we get:
d = √(ε₀AV / σ)
Plugging in the values we know, we get:
d = √((8.854 x 10^-12 F/m)(0.025 m²)(150 V)) / (30 x 10^-9 C/m²)) = 1.00 x 10^-4 m
Therefore, the spacing between the plates is 1.00 x 10^-4 m.