Lesson 30 Capacitance and Potential

In 1745, Pieter van Musschenbroek, wanted to make an electric field solution and developed the Leyden jar.

Benjamin Franklin interpreted the Lyden jar and developed an electric theory concerning charge.

In the vacinity of a positive charge, the electric force repels a positive test charge, and an external force is needed to push the charge closer doing work against the electrical force, a positive force (work) if the component does work that is opposite to the electric force. 

dW = -F dr

It is known as negative work if it has a component along the force and no work at all if the motion is perpendicular to the electric force.

The net work is found by

integral (dw) = integral (-F dr)

delta (w) = -integral (F dr)

The net work is delta (U) or the change in potential energy of the test charge.

delta (U) = -integral ( F dr)

F = qE

The electric force is the charge multiplied by the electric field.

delta (U) = q delta (V)

delta (V) = -integral (E dr) or the change in electric potential concerning only the path of the charge through the field. it is measured in volts.

Before the electric field, Franklin theorized the electric atmosphere where all objects contain electrical fluid, where objects with too much fluid have a positive charge and objects with too little fluid have a negative charge. Franklin understood that electric charge in never created nor destroyed, but flows from one object to the next.

All objects with a net electrical charge produce an electricl field. If objects contain both positive and negative charges, the electric field exists, but is small in nature, and renders the object with a neutral charge. Inside metals, there is not static electricity because all the charged atoms of the metal are attracted to the surface and prevent further movement.

positive charge: >U
negative charge: <U
where q is proportional to V

A battery can create an electric field where -- as electricity flows between two conductors -- the difference in potential energy is equivalent to the voltage of the battery, and creates an electric field.

q = CV

The charge transfered is proportional to the voltage applied, and the constant of proportionality is C (capacitance).

Franklin revolutionized physics by discovering that electric force is neither created nor destroyed, but transfered from source to source according to the electric charge.

A capacitor can be made with any two pieces of metal. A parallel plate capacitor with two sheets of opposite charge create an electric field between themselves, with the total amount of voltage proportional to distance between the two plates. A parallel plate capacitor was present within Leyden jars.