Electric Field and Electric Potential

Understand the meaning and significance of electric potential.

Use the electric potential to calculate the electric field.

Use integration to determine electric potential difference between two points on a line, given electric field strength as a function of position along that line.

Calculate how much work is required to move a test charge from one location to another in the field of fixed point charges.

Express in equation form the energy stored in a capacitor.
Electric Field:
Electric field is defined as the electric force per unit charge. Electric field is also known as electrostatic field intensity.
Electric field from a point charge:
The electric field a distance r away from a point charge q is given by:
\[E = \dfrac{k q}{r^2}\]
The electric field from a positive charge points away from the charge; the electric field from a negative charge points toward the charge. Like the electric force, the electric field E is a vector. If the electric field at a particular point is known, the force a charge q experiences when it is placed at that point is given by :
\[F = QE\]
Electric Potential:
Electric potential is more commonly known as voltage. The potential at a point a distance r from a charge q is given by: \[V = \dfrac{k q}{r}\] Electric potential, like potential energy, is a scalar, not a vector.
SI unit for electric potential:
1 Volt = 1 Joule/1 Coulomb or \[V = \dfrac{J}{C}\] (The number of volts indicates the number of joules work or energy per coulomb.)
Potential Difference:
Electric potential difference is the difference in electric potential (V) between the final and the initial location when work is done upon a charge to change its potential energy.
In equation form, the electric potential difference is: \[\Delta V = V_B  V_A = \dfrac{W_{B \rightarrow A}}{q}\] Conventional current flows around a circuit from the positive (+) side of the cell to the negative (). However the electrons are flowing around the circuit in the opposite direction from the negative () side of the cell to the positive (+).
Energy Stored in a Capacitor
\[E = \dfrac{1}{2}CV^2 = \dfrac{QV}{2} = \dfrac{Q^2}{2C}\] where Q is the charge and V the voltage on a capacitor C.