Electric Charge, Fields, Potential and Current
Electric Charge and Electric Field
Electric charge — it is a property of a body; charged bodies exhibit attraction and repulsion.
Electric field
Electric field — the sphere around a source charge in which a test charge would experience a force is called the electric field.
Electric field lines
Electric field lines — an electric field is represented by imaginary lines of force which are called electric field lines.
Properties of field lines
- They are imaginary lines of force.
- They are not closed (they begin and end on charges).
Mathematical definition of electric field
The electrostatic force per unit test charge is called the electric field. i.e. E = F / q0.
Electric dipole
Electric dipole — an electric dipole consists of two equal and opposite charges separated by a small distance.
Dipole moment
Electric dipole moment — it is equal to the product of the magnitude of either charge and the dipole length.
i.e. p = q × 2l. SI unit: coulomb metre (C·m).
Ideal dipole
Ideal dipole — an electric dipole is ideal if its dipole length tends to zero while the dipole moment remains finite (i.e., 2l → 0).
Electric flux
Electric flux — the number of electric field lines passing through a surface normally is called electric flux.
Mathematically it is equal to the dot product of the electric field E and the surface area S: Φ = E · S.
Gauss’s law of electrostatics
Gauss’s law — the electric flux linked with a closed surface is equal to 1/ε0 times the total charge enclosed by the surface.
Electric Potential and Capacitance
Electrostatic potential
Electrostatic potential (V) — an electrostatic potential at any point in the region of an electric field is equal to the amount of work done in bringing a unit positive test charge (without acceleration) from infinity to that point.
i.e. V = W / q0. SI unit: volt (V).
Electric potential difference
Electric potential difference (EPD) — the potential difference between two points inside an electric field is defined as the work done in displacing a unit positive test charge from the point of lower potential to the point of higher potential.
Potential at A = VA (low)
Potential at P = VP (high)
Potential difference between the two points: V = VP – VA = W / q0. SI unit: volt (V).
Current Electricity
Electric current
Electric current (I) — the rate of flow of charge through a conductor is called electric current.
Mathematically, I = q / t. SI unit: ampere (A).
Conventional current
Conventional current — by conventional current, the direction of flow of positive charge in a conductor is taken as the direction of current; this is opposite to the direction of flow of electrons.
Electric circuit
Electric circuit — a continuous and closed path of electric current is called an electric circuit.
Potential difference in a conductor
Potential difference (PD) between two points in a current-carrying conductor is defined as the amount of work done in displacing a unit charge from one point to another.
V = W / Q. SI unit: volt (V).
Ohm’s law
Ohm’s law — at constant temperature, the potential difference applied across a conductor is directly proportional to the current flowing through it.
V is directly proportional to I
V = I R
Resistivity (specific resistance)
Specific resistance (resistivity) — the resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area.
i.e. R is directly proportional to L
and R is inversely proportional to area A
Combining: R is proportional to L / A, so R = ρ × L / A
Temperature dependence of resistivity
Temperature dependence of resistivity — resistivity of a substance depends on the number density n of charge carriers and the relaxation time τ as:
ρ = m / (n e2 τ)
Electromotive force (EMF)
EMF (electromotive force) — the maximum potential difference between the terminals of a cell when no current is drawn from the cell (i.e., when the cell is in open circuit). SI unit: volt (V).
Terminal potential difference
Terminal potential difference of a cell (V) — the potential between the terminals of a cell when current flows through the circuit is called the terminal potential difference. SI unit: volt (V).