D.2.1 Electric field properties and laws

Electric Charge

Positive and Negative Charges

Electric charge is a fundamental property of matter, existing in two types: positive and negative.

Note

Protons carry a positive charge, while electrons carry a negative charge of equal magnitude.

Example

When you rub a plastic rod with a wool cloth, electrons transfer from the wool to the rod.
The rod becomes negatively charged, while the wool becomes positively charged.

Conservation of Charge

The total charge in an isolated system remains constant.

Example

If two spheres with charges of +4 μC and -2 μC touch and then separate, the total charge remains +2 μC. Each sphere ends up with +1 μC.

Quantisation of Charge

Charge is quantised, meaning it exists in discrete units of the elementary charge $e = 1.6 \times 10^{- 19} C$ .

Note

The charge of any object is always an integer multiple of $e$ .

Coulomb’s Law

Coulomb’s law describes the electric force between two point charges.
The force $F$ between two charges $q_{1}$ and $q_{2}$ separated by a distance $r$ is given by:

$F = k \frac{q_{1} q_{2}}{r^{2}}$

where $k$ is the Coulomb constant:

$k = \frac{1}{4 π ϵ_{0}} \approx 8.99 \times 10^{9} {N m}^{2} / C^{2}$

Hint

$ϵ_{0}$ is the permittivity of free space, with a value of $8.85 \times 10^{- 12} C^{2} / {N m}^{2}$ .

Properties of the Electric Force

Attractive or Repulsive:
- Like charges repel; opposite charges attract.
Vector Quantity:
- The force acts along the line joining the two charges.
Inverse Square Law:
- The force decreases with the square of the distance between the charges.

Common Mistake

A common mistake is to forget that the force is mutual.

If $q_{1}$ exerts a force on $q_{2}$ , $q_{2}$ exerts an equal and opposite force on $q_{1}$ .

Example question

Electric Force

Two charges, $q_{1} = 2.0 μ C$ and $q_{2} = 8.0 μ C$ , are 3.0 cm apart. Calculate the electric force between them.

Solution

$F = 8.99 \times 10^{9} \times \frac{2.0 \times 10^{- 6} \times 8.0 \times 10^{- 6}}{(0.03)^{2}}$

$= 160 N$

This force is repulsive because both charges are positive.

Electric Field Strength

Definition

Electric field

An electric field is a region of space where a charge experiences a force.

Definition

Electric field strength

The electric field strength $E$ is defined as the force per unit charge experienced by a small positive test charge $q$ .

It is expressed by the formula:

$E = \frac{F}{q}$

Note

The unit of electric field strength is newtons per coulomb $N C^{- 1}$ .

Electric Field Due to a Point Charge

The electric field strength $E$ at a distance $r$ from a point charge $Q$ is given by:

$E = k \frac{Q}{r^{2}}$

Example

Electric field strength

A charge of +5.0 μC creates an electric field. At a point 0.2 m away, the field strength is:

$E = 8.99 \times 10^{9} \times \frac{5.0 \times 10^{- 6}}{(0.2)^{2}}$
$= 1.12 \times 10^{6} {N C}^{- 1}$

Field Line Representation

Direction of Field Lines

Field lines originate from positive charges and terminate at negative charges.
The direction of the field line at any point shows the direction of the force on a positive test charge.

Density of Field Lines

The density of field lines indicates the strength of the electric field:

Closer ines represent a stronger field.
Farther apart lines represent a weaker field.

Electric field lines for different charges.

Example

In a uniform electric field between two parallel plates, the field lines are equally spaced, indicating constant field strength.
Near a point charge, the lines spread out, showing the field weakens with distance.

Tip

Field lines never cross.
If they did, it would imply two different directions for the electric field at the same point, which is impossible.

Reflection

Theory of Knowledge

How does the concept of a field help us understand "action at a distance"? Could this idea apply to other forces, like gravity or magnetism?

Electric fields are fundamental to understanding how charges interact, laying the groundwork for technologies like electric motors, capacitors, and semiconductors.

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