The Leyden jar, invented by chance in 1746, was one of the earliest types of cap

Question

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 19 cm and radius 6 cm, made of 3 mm thick Pyrex glass. (The dielectric strength of the Pyrex glass is 1.00 107 V/m.) (b) What is the maximum charge that could be stored on it?

Explanation / Answer

formula capacitence of a cylindrical capacitor is

C = 2pi eo L/ log ( b/a)

= 2 * 3.14 * 8.85 * 10^-12 ( 0.19 m)/ log ( 0.06+0.003/0.06)

=0.498 * 10^-9 F

(b)

Q= CV

= C (Ed)

= 0.498 * 10^-9 F( 1.0* 10^7 V/m) ( 0.06+0.003) = 3.13 * 10^-4 C

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