A parallel-plate capacitor is made from two aluminum-foil sheets, each 3.90 cm wide and 10.3 m long. Between the sheets is a mica strip of the same width and length that is 0.0225 mm thick. What is the maximum charge that can be stored in this capacitor? (The dielectric constant of mica is 5.4, and its dielectric strength is 1.00 108 V/m.) Please help soon. I feel like this should have been easy, but its not.
To find the maximum charge that can be stored in the capacitor, we need to calculate the capacitance of the capacitor first and then use the formula Q = CV, where Q is the charge stored, C is the capacitance, and V is the voltage applied.
To calculate the capacitance of the parallel-plate capacitor, we can use the formula:
C = ε₀ * (A / d),
where C is the capacitance, ε₀ is the vacuum permittivity (8.85 x 10^-12 F/m), A is the area of the plates, and d is the distance between the plates.
Since the capacitor has two aluminum-foil sheets with a mica strip between them, the area of the plates is given by:
A = width * length,
A = (3.90 cm * 10.3 m).
Before we can use this value, we need to convert the width to meters:
width = 3.90 cm = 3.90 x 10^-2 m.
So, the area becomes:
A = (3.90 x 10^-2 m * 10.3 m).
Now, we need to calculate the distance between the plates. The thickness of the mica strip is given as:
d = 0.0225 mm = 0.0225 x 10^-3 m.
Now we can calculate the capacitance:
C = ε₀ * (A / d),
C = (8.85 x 10^-12 F/m) * ((3.90 x 10^-2 m * 10.3 m) / (0.0225 x 10^-3 m)).
By evaluating this expression, we get the value of capacitance.
Now, to calculate the maximum charge that can be stored in the capacitor, we use the formula:
Q = CV.
To find the maximum voltage that can be applied, we use the formula:
V = εr * E,
where V is the maximum voltage, εr is the relative permittivity of the dielectric material (in this case, mica), and E is the electric field strength.
The electric field strength E can be calculated using:
E = V / d,
where d is the distance between the plates.
Given that the dielectric strength of mica is 1.00 x 10^8 V/m, we have:
E = (1.00 x 10^8 V/m) * (0.0225 x 10^-3 m).
Now we have the electric field strength E. Substituting this value into the equation V = εr * E, where εr is 5.4 (the dielectric constant of mica), we can find the maximum voltage V.
Finally, substitute the capacitance C and maximum voltage V values into the formula Q = CV to get the maximum charge Q that can be stored in the capacitor.
By following these steps, you should be able to find the maximum charge that can be stored in the capacitor.