Long Summary

22.1 Field Patterns

Charging Objects

• Charging by Rubbing:

  • Most plastic materials can be easily charged by rubbing with a dry cloth.

  • A charged piece of plastic can attract small bits of paper.

• Attraction and Repulsion:

  • Like charges repel; unlike charges attract.

  • Example: A charged perspex ruler attracts a charged polythene comb, but two charged rods of the same material repel each other.

• Role of Electrons:

  • Electrons are primarily responsible for charging.

  • An uncharged atom has equal numbers of protons and electrons.

  • To negatively charge an atom, add electrons; to positively charge, remove electrons.

Conductors and Insulators

• Electrical Conductors:

  • Metals contain many free electrons that can move throughout the material.

  • To charge a metal, it must be isolated from the Earth. If not, any charge can be neutralized due to electron transfer with Earth.

  • When in direct contact with a charged object, an isolated conductor can gain charge.

• Earthing a Conductor:

  • If a positively charged conductor is earthed, electrons will flow from the Earth to neutralize the charge.

• Electrical Insulators:

  • Insulating materials do not have free electrons.

  • Electrons remain attached to individual atoms.

  • Insulators like perspex or polythene are easier to charge due to their atomic structure.

Shuttling Ball Experiment

• Setup:

  • A conducting ball hangs on an insulating thread between two plates.

  • A high voltage is applied across these plates, causing the ball to shuttle between them.

• Mechanism:

  • Each time the ball contacts the negative plate, it gains electrons and becomes negatively charged.

  • Afterwards, it is repelled to the positive plate, transferring the electrons to the positive plate and becoming positively charged.

• Current Generation:

  • The microammeter measures current due to electrons moving through the circuit.

  • As the plates are brought closer, the frequency of the ball's shuttling increases, causing higher current readings.

Electric Field Lines

• Representation of Electric Fields:

  • Electric fields can be illustrated using field lines, indicating both the magnitude and direction of the electric field.

• Direction of Field Lines:

  • A line of force in an electric field shows the direction a positive test charge would move.

  • In situations where multiple charges are involved, the resultant electric field is the vector sum of fields from each charge.

• Field Patterns:

  • Opposite charges attract, creating concentrated field lines.

  • For plates, lines show a uniform electric field between them.

• Examples of Electric Field Patterns:

  • Oppositely charged points create concentrated field lines (Figure 6a).

  • A point charge near a plate has field lines concentrated at the charge (Figure 6b).

  • Parallel plates create uniform field lines (Figure 6c).

22.2 Electric Field Strength

Learning Objectives:

• Describe how to measure, in principle, the strength of an electric field.

• Discuss whether electric field strength E is a scalar or a vector and describe how this affects the sign of a test charge to use.

• Explain why E should be described as the force per unit charge instead of the force that acts on one coulomb of charge.
  Specification reference: 3.7.3.2

Definition and Measurement of Electric Field Strength

• Electric Field Strength (E):

  • Defined as the force per unit charge on a positive test charge at a given point in an electric field.

  • Units: Newton per Coulomb (NC⁻¹).

  • Formula:
    $E = \frac{F}{Q}$
    where F is the force and Q is the test charge.

  • Rearranged: $F = QE$, indicating the force on a test charge.

• Direction of E:

  • E is a vector pointing in the same direction as the force on a positive charge.

  • For positive charges, the force is in the same direction as E; for negative charges, in the opposite direction.

Worked Example

• Given:

  • Test charge Q = 3.5 μC

  • Force F = 70 mN

• Calculate E:
  $E = \frac{70 \times 10^{-3}}{3.5 \times 10^{-6}} = 2.0 \times 10^4 \text{ NC}^{-1}$

22.3 Electric Potential

Learning Objectives:

• Explain why potential is defined in terms of the work done per unit positive charge.

• Describe how to find the change in electric potential energy from potential difference (pd).

• Explain why potential (and pd) is measured in volts (V).
  Specification reference: 3.7.3.3

Electric Potential Definition

• Electric Potential (V):

  • Work done per unit charge in moving a positive test charge from infinity to that position.

  • Units: Volts (V), defined as 1 J/C.

  • Formula for potential energy (Ep) of a test charge Q at position P:
    $V = \frac{E_p}{Q}$

• Change in Potential Energy:

  • $\Delta W = Q(V<em>2 - V</em>1)$

  • Where the change in electric potential energy is calculated by the difference in potential.

Example Calculation

• Calculate the potential energy of a +1 μC charge at a potential of -1000 V:
  $E_p = QV = 1.0 \times 10^{-6} \times -1000 = -1.0 \times 10^{-3} J$

22.4 Coulomb's Law

Learning Objectives:

• Describe how the force between two point charges depends on distance.

• Calculate the force between two charged objects.

• Explain what the sign of the force indicates.
  Specification reference: 3.7.3.1

Coulomb's Experiment

• Coulomb's Law:

  • The force (F) between two point charges (Q₁ and Q₂) is given by
    $F = k \frac{Q<em>1 Q</em>2}{r^2}$
    where k is Coulomb's constant.

• Force Behavior:

  • Like charges repel, unlike charges attract.

  • The force increases as the charges move closer (inverse-square law).

• Example Calculation:

  • If Q₁ is a proton (+1.6 × 10⁻¹⁹ C) and Q₂ is an electron (-1.6 × 10⁻¹⁹ C) at a distance of 3.00 x 10⁻¹⁰ m, calculate:
    $F = \frac{(1.6 \times 10^{-19})(-1.6 \times 10^{-19})}{4\pi(8.85 \times 10^{-12})(3.00 \times 10^{-10})^2}$
    (F = 2.56 \times 10^{-9} N)

Key Relationships

• Electric Field Strength (E):

  • $E = k\frac{Q}{r^2}$

• Electric Potential (V):

  • $V = k\frac{Q}{r}$

Synoptic Links

Comparison with Gravitational Fields

• Electric fields are analogous to gravitational fields in that both follow inverse-square laws.

• The electric force can be significantly stronger than gravitational force, illustrated by the electrostatic force between a proton and an electron being approximately $2.3 \times 10^{39}$ times stronger than the gravitational force.

22.5 Point Charges and Fields

• General Behavior:

  • Electric fields surround any charged object, with more charge resulting in a stronger field.

• Sparks and Shocks:

  • High concentrations of charge can lead to ionisation of air and subsequent discharge (e.g., lightning).

• Field Dynamics:

  • Field lines diverge from positive charges and converge towards negative charges.

• Understanding Forces:

  • When multiple charges are present, their field contributions are summed to determine the resultant force on a test charge.

• Proportions:

  • The electric field between parallel plates is uniform and the electric field strength E is equal to the potential difference per unit distance:
    $E = \frac{V}{d}$

Summary of Key Formulas

• Electric Field Strength:
  $E = \frac{F}{Q}$

• Coulomb's Law:
  $F = k \frac{Q<em>1 Q</em>2}{r^2}$

• Electric Potential:
  $V = \frac{E_p}{Q}$

• Work Done by Electric Field:
  $\Delta W = Q(V<em>2 - V</em>1)$

Conclusion

• Electric fields are crucial in understanding electrostatics and the interactions between charged particles, forming the foundation for many concepts in physics and engineering today.