Electric Charge
Positive and Negative Charges
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.
Conservation of Charge
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.
Quantization of Charge
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 $e$.
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:
$$k = \frac{1}{4\pi \epsilon_0} \approx 8.99 \times 10^9 \, \text{N m}^2 \ \text{C}^{-2}$$
$\epsilon_0$ is the permittivity of free space, with a value of $8.85 \times 10^{-12} \, \text{C}^2 \ \text{N m}^{-2}$.
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.
- 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.
Coulomb's Law
Electric Field Strength
Electric field
An electric field is a region of space where a charge experiences a force.
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:
$$E = \frac{F}{q}$$
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:
$$E = k \frac{Q}{r^2}$$
- 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 Line Representation
Direction and Density 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.
- 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.
