Electric Potential Difference

An electric field is a region in space where a force is exerted on a positive test charge .

Electric lines of force represent the direction that a positive test charge would move in an electric field.

• By convention, they originate at positively charged objects and terminate at negatively charged objects.

A charge in an electric field experiences an electric force.
Work
is done by the electric field if the electric force acting on the charge causes it to move from one point to another.
• These two points differ in their electric potential.
If the electrical force moves a charge a certain distance, it does work on that charge. The change in electric potential over this distance is defined through the work done by this force: Work = Force x distance = (charge on Q) x (Potential) where potential is shorthand for change in electric potential, or potential difference .

This is analogous to the definition of the gravitational potential energy through the work done by the force of gravity in moving a mass through a certain distance.

The units of potential difference, or simply potential, are Joules / Coulomb, which are called Volts (V).

• Physically, potential difference has to do with how much work the electric field does in moving a charge from one place to another.
• Batteries, for example, are rated by the potential difference across their terminals.
• In a nine volt battery the potential difference between the positive and negative terminals is precisely nine volts.
• On the other hand the potential difference across the power outlet in the wall of your home is 110 volts.
The magnitude of the work done on the charge by the electric field is a measure of the difference in potential.
The electric potential difference (V) is the work done per unit charge as a charge is moved between two points in an electric field.

V = W ÷ Q

The volt (V) is the unit used to measure electric potential difference.

An electric potential difference must exist for current to flow in an electric circuit.

As charge moves from one point to another in an electric circuit, energy is released.

• This results in a decrease in electric potential.
• The decrease in electric potential implies that there is an electric potential difference between the two points.
• The term electric potential difference is preferable to "voltage."
The potential of the earth is arbitrarily said to be zero.

An object connected directly to the ground can be described as being earthed, or “grounded”.

The potential at any point in an electric field can be either positive or negative with respect to the earth, depending on the nature of the charge (pos or neg).

Capacitance

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The capacitance is usually defined as the total electric charge placed on the object divided by the potential of the object:

C = Q ÷ V

where

C is the capacitance in farads

Q is the charge in coulombs

V is the potential in volts

Note that this formula results in "charge per volt", or Coulombs per volt. 1 Coulomb/volt equals 1 farad..

Capacitance exists between any two conductors insulated from one another.

The formula defining capacitance above is valid if it is understood that the conductors have equal but opposite charge Q, and the voltage V is the potential difference between the two conductors.

The SI unit of capacitance is the farad (F).

A capacitance of one farad results in a potential of one volt for one coulomb of charge.

The capacitance of the majority of capacitors used in electronic circuits is several orders of magnitude smaller than the farad.

The most common units of capacitance in use today are the microfarad (µF), the nanofarad (nF) and the picofarad (pF).

It should be noted that the above equation (C = Q/V) is only applicable for values of Q which are much larger than the electron charge e = 1.602x10-19 C.

For example, if a capacitance of 1 pF is charged to a voltage of 100 nV, the equation would predict a charge Q = 10-19 C, which is smaller than the charge on a single electron.

Homework: Ch 21, problems 32-36, 39,40,41

Video: Electric Potential and Capacitance