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
Hmmm.
a. Electric Field= potentialDifference/distance
b. C=epsilion*area/distance=q/V
q/area=epsilion*Voltage/distance
c. see b. solve for C
d. solve for q.
To answer these questions, we need to use the formulas related to capacitors. Let's go step by step:
(a) To calculate the electric field between the plates, we can use the formula:
Electric Field (E) = Voltage (V) / Separation Distance (d)
Given:
Voltage (V) = 16.0 V
Separation Distance (d) = 1.70 mm = 0.0017 m
Plugging in the values:
E = 16.0 V / 0.0017 m = 9411.76 V/m
Therefore, the electric field between the plates is 9411.76 V/m.
(b) The surface charge density (σ) is given by the formula:
Surface Charge Density (σ) = Electric Field (E) * Permittivity of Free Space (ε0)
The permittivity of free space (ε0) is a constant value of approximately 8.85 x 10^-12 F/m.
Plugging in the values:
σ = 9411.76 V/m * 8.85 x 10^-12 F/m = 8.33 x 10^-8 C/m^2
Therefore, the surface charge density is 8.33 x 10^-8 C/m^2.
(c) The capacitance (C) of the capacitor can be found using the formula:
Capacitance (C) = (Permittivity of Free Space (ε0) * Area of Plates (A)) / Separation Distance (d)
Given:
Area of Plates (A) = 7.60 cm^2 = 0.00076 m^2
Separation Distance (d) = 1.70 mm = 0.0017 m
Plugging in the values:
C = (8.85 x 10^-12 F/m * 0.00076 m^2) / 0.0017 m = 3.95 x 10^-12 F = 3.95 pF
Therefore, the capacitance is 3.95 pF.
(d) The charge on each plate (Q) can be calculated using the formula:
Charge (Q) = Capacitance (C) * Voltage (V)
Given:
Capacitance (C) = 3.95 pF = 3.95 x 10^-12 C
Voltage (V) = 16.0 V
Plugging in the values:
Q = 3.95 x 10^-12 C * 16.0 V = 6.32 x 10^-11 C = 63.2 pC
Therefore, the charge on each plate is 63.2 pC.