Electricity and Magnetism · Problem 10.16
MAGNETIC FIELDS IN MATTER — Edward Purcell & David Morin
Physics — E&M · capacitance-dielectric
Problem
In 1746 a Professor Musschenbroek in Leiden charged water in a bottle by touching a wire, projecting from the neck of the bottle, to his electrostatic machine. When his assistant, who was holding the bottle in one hand, tried to remove the wire with the other, he got a violent shock. Thus did the simple capacitor force itself on the attention of electrical scientists. The discovery of the ``Leyden jar'' revolutionized electrical experimentation. In 1747 Benjamin Franklin was already writing about his experiments with ``Mr. Musschenbroek's wonderful bottle.'' The jar was really nothing but glass with a conductor on each side of it. To see why it caused such a sensation, estimate roughly the capacitance of a jar made of a 1 liter bottle with walls 2 mm thick, the glass having a dielectric constant 4. What diameter sphere, in air, would have the same capacitance?Intuitive explanation
The Leyden jar works because glass between two conductors—even a thin layer—creates a capacitor with surprisingly large capacitance due to the dielectric constant. You'll calculate the jar's capacitance using the parallel-plate formula adapted for a cylindrical geometry, then find what size isolated conducting sphere would store the same charge at the same voltage. The key insight is that a small, practical device can rival the capacitance of a sphere meters across, which explains why it shocked people—it could accumulate and suddenly release substantial charge.
Intuitive explanation
The Leyden jar works because glass between two conductors—even a thin layer—creates a capacitor with surprisingly large capacitance due to the dielectric constant. You'll calculate the jar's capacitance using the parallel-plate formula adapted for a cylindrical geometry, then find what size isolated conducting sphere would store the same charge at the same voltage. The key insight is that a small, practical device can rival the capacitance of a sphere meters across, which explains why it shocked people—it could accumulate and suddenly release substantial charge.