An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2, separated by a distance of 1.70 mm.
(a) If a 16.0 V potential difference is applied to these plates, calculate the electric field between the plates.
kV/m
(b) What is the surface charge density?
nC/m2
(c) What is the capacitance?
pF
(d) Find the charge on each plate.
pC
To calculate the electric field between the plates of an air-filled capacitor, we can use the formula:
E = V/d
where:
E is the electric field,
V is the potential difference, and
d is the distance between the plates.
(a) Given that the potential difference (V) is 16.0 V and the distance between the plates (d) is 1.70 mm, we can calculate the electric field (E) using the formula:
E = V/d = 16.0 V / 1.70 mm
First, let's convert the distance from millimeters (mm) to meters (m):
1.70 mm = 1.70 x 10^(-3) m
Now, we can calculate the electric field:
E = 16.0 V / 1.70 x 10^(-3) m
Solving this equation gives us the electric field between the plates in kilovolts per meter (kV/m).
(b) To find the surface charge density, we can use the formula:
σ = ε₀E
where:
σ is the surface charge density,
ε₀ is the permittivity of free space (8.85 x 10^(-12) F/m), and
E is the electric field.
Given that the electric field (E) was calculated in part (a), we can now substitute the values into the formula:
σ = 8.85 x 10^(-12) F/m x E
This will give us the surface charge density in nanocoulombs per square meter (nC/m²).
(c) The capacitance (C) of a parallel plate capacitor can be calculated using the formula:
C = ε₀A/d
where:
C is the capacitance,
ε₀ is the permittivity of free space (8.85 x 10^(-12) F/m),
A is the area of each plate, and
d is the distance between the plates.
Given that the area (A) of each plate is 7.60 cm² and the distance (d) between the plates is 1.70 mm, we need to convert these values to the appropriate units before substituting them into the formula:
7.60 cm² = 7.60 x 10^(-4) m²
1.70 mm = 1.70 x 10^(-3) m
Now, we can calculate the capacitance using the formula:
C = 8.85 x 10^(-12) F/m x (7.60 x 10^(-4) m²) / (1.70 x 10^(-3) m)
This will give us the capacitance in picofarads (pF).
(d) To find the charge on each plate, we can use the formula:
Q = CV
where:
Q is the charge,
C is the capacitance, and
V is the potential difference.
Given that the capacitance (C) and potential difference (V) were calculated in parts (c) and (a) respectively, we can substitute the values into the formula:
Q = C x V
This will give us the charge on each plate in picocoulombs (pC).