The Leyden jar, invented by chance in 1746, was one of the earliest types of capacitors (see the figure below), made by covering the inner and outer surfaces of a glass jar with conducting layers (for example, aluminum foil). It is a good approximation to treat the Leyden jar as a parallel-plate capacitor.

(a) Find the capacitance for a cylindrical jar of height 18 cm and radius 6 cm, made of 3 mm thick Pyrex glass. (The dielectric strength of the Pyrex glass is 1.00*10^7 V/m.)

(b) What is the maximum charge that could be stored on it?

To find the capacitance of the Leyden jar, we can use the formula for the capacitance of a parallel-plate capacitor. The formula is:

C = (ε₀ * εᵣ * A) / d,

where:
C is the capacitance,
ε₀ is the permittivity of free space (8.85 * 10^(-12) F/m),
εᵣ is the relative permittivity of the dielectric material (also known as the dielectric constant) of the glass,
A is the area of one plate,
d is the distance between the plates.

Let's calculate the capacitance:

(a) First, we need to find the area of one plate. The area of a cylinder is given by the formula:

A = 2πrh + πr^2,

where:
r is the radius of the cylinder (6 cm = 0.06 m),
h is the height of the cylinder (18 cm = 0.18 m).

A = 2π(0.06 m)(0.18 m) + π(0.06 m)^2
A = 0.216π m^2 + 0.0036π m^2
A = 0.2196π m^2.

(b) Next, we need to calculate the capacitance using the given thickness of the glass (3 mm = 0.003 m) and the relative permittivity of Pyrex glass (εᵣ = 1).

C = (ε₀ * εᵣ * A) / d
C = (8.85 * 10^(-12) F/m) * (1) * (0.2196π m^2) / (0.003 m)
C = 5.17 * 10^(-11) F.

So, the capacitance of the Leyden jar is approximately 5.17 * 10^(-11) F.

(b) To find the maximum charge that could be stored on the Leyden jar, we can use the formula:

Q = C * V,

where:
Q is the charge,
C is the capacitance,
V is the voltage.

Since the maximum voltage that the Pyrex glass can withstand is given as 1.00 * 10^7 V/m, we can use this as the maximum voltage.

Q = (5.17 * 10^(-11) F) * (1.00 * 10^7 V)
Q = 5.17 * 10^(-4) C.

Therefore, the maximum charge that could be stored on the Leyden jar is approximately 5.17 * 10^(-4) C.