Electric charge is a fundamental property of matter, existing in two types: positive and negative.
Protons carry a positive charge, while electrons carry a negative charge of equal magnitude.
- 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.
The total charge in an isolated system remains constant.
- 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.
Charge is quantized, meaning it exists in discrete units of the elementary charge $e = 1.6 \times 10^{-19} \, \text{C}$.
The charge of any object is always an integer multiple of $e$.
- Robert Millikan measured the charge on tiny oil droplets held between two charged plates, balancing the electric force against gravity.
- Every droplet carried a charge that was a whole-number multiple of e, which is the direct evidence that charge is quantized.
Objects become charged when electrons move between them. Protons stay fixed in the nucleus, so it is always electrons that transfer.
- Charging by friction
- Rubbing two materials together transfers electrons from one to the other, so a plastic rod rubbed with wool becomes negatively charged.
- Charging by contact
- A charged object touching a conductor shares its charge, leaving both with the same sign of charge.
- Charging by induction
- Bringing a charged object near a conductor makes the free charges inside separate, without any contact.
- If the conductor is then grounded, electrons flow to or from the Earth, leaving it with a net charge opposite in sign to the object.
- Grounding connects an object to the Earth, which acts as an unlimited reservoir of electrons.
- Electrons flow until the object reaches the required charge or becomes neutral.
- 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:
$$k = \frac{1}{4\pi \epsilon_0} \approx 8.99 \times 10^9 \, \text{N m}^2 \ \text{C}^{-2}$$
$\epsilon_0$ is the permittivity of free space, with a value of $8.85 \times 10^{-12} \, \text{C}^2 \, \text{N}^{-1} \, \text{m}^{-2}$.
- 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.
- 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 $q_1$.
Two charges, $q_1 = 2.0 \, \mu\text{C}$ and $q_2 = 8.0 \, \mu\text{C}$, are 3.0 cm apart. Calculate the electric force between them.
Solution
$$F = 8.99 \times 10^9 \times \frac{2.0 \times 10^{-6} \times 8.0 \times 10^{-6}}{(0.03)^2} $$
$$= 160 \, \text{N}$$
This force is repulsive because both charges are positive.
It is expressed by the formula:
$$E = \frac{F}{q}$$
The unit of electric field strength is newtons per coulomb $N \, C^{-1}$.
The electric field strength $E$ at a distance $r$ from a point charge $Q$ is given by:
$$E = k \frac{Q}{r^2}$$
- A charge of +5.0 μC creates an electric field.
- At a point 0.2 m away, the field strength is:
$$E = 8.99 \times 10^9 \times \frac{5.0 \times 10^{-6}}{(0.2)^2}$$
$$ = 1.12 \times 10^6 \, \text{N C}^{-1}$$
- 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.
- The density of field lines indicates the strength of the electric field:
- Closer lines represent a stronger field.
- Farther apart lines represent a weaker field.
- 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.
- Field lines never cross.
- If they did, it would imply two different directions for the electric field at the same point, which is impossible.
- What are the two types of electric charge, and which particles carry each type?
- State Coulomb's law and describe how the force changes when the separation between two charges doubles.
- What did Millikan's oil-drop experiment demonstrate about electric charge?
- Name the three methods of charging an object.
- What does the spacing of electric field lines tell you about the strength of the field?