(a) It a drop of liquid has capacitance 1.00 pF, what 15 its...

(a) It a drop of liquid has capacitance $1.00 \mathrm{pF}$, what 15 its radius? (b) If another drop has radius $2.00 \mathrm{~mm}$, what is its capacitance? (c) What is the charge on the smaller drop if its potential is $100 \mathrm{~V} ?$

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Key Concepts

Capacitance of a Sphere

This concept involves understanding that an isolated conductive sphere has a capacitance determined by its geometry and the permittivity of the surrounding medium. The formula C = 4???R links the capacitance to the sphere's radius, making it possible to calculate one when the other is provided. This relationship underpins many problems in electrostatics, especially when approximating objects like liquid drops as spherical conductors.

Charge-Potential Relationship

This principle is fundamental in electrostatics, where the charge stored on a conductor is directly related to its capacitance and the potential (voltage) it is held at, by the equation Q = C V. This relation enables the determination of the amount of electric charge on an object when its capacitance and the potential difference are known.

Spherical Conductor Approximation

Many problems, particularly those involving small liquid droplets or particles, approximate the object as a perfect spherical conductor to simplify calculations. This approximation allows for the application of established formulas such as C = 4???R and Q = C V, making it easier to analyze electrostatic phenomena in realistically complex systems.

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