State that the direction of an electric field at a point is the direction of the force on a positive charge at that point

4.2.1 Electric Charge

Learning Objectives

1. Define positive and negative electric charge.
2. Explain how friction transfers only electrons and therefore produces charge.
3. Describe a simple experiment for detecting static charge.
4. State the law of charge conservation.
5. Identify the SI unit of charge (coulomb, C) and the symbols used ( q or Q ).
6. Recall that charge is quantised in integer multiples of the elementary charge \(e\).
7. Define the electric field \(\mathbf{E}\) and state that its direction is the direction of the force on a positive test charge.
8. Interpret basic electric‑field‑line diagrams (point charge, charged sphere, parallel‑plate capacitor).
9. Apply \(\mathbf{E}= \mathbf{F}/q_{\text{test}}\) to a simple numerical problem.

1. What is Electric Charge?

Electric charge is a fundamental property of matter. An object may have a net positive charge, a net negative charge, or be electrically neutral (no net charge).

2. Production of Charge by Friction (Electrostatic Generation)

• When two different insulating materials are rubbed together, electrons are transferred from one surface to the other.
• Only electrons (negative charge) move; the material that loses electrons becomes positively charged, the material that gains electrons becomes negatively charged.
• Example: Rubbing a glass rod with silk removes electrons from the glass, leaving the glass positively charged and the silk negatively charged.

3. Detecting Static Charge

A simple way to detect static charge is with an electroscope:

• Bring a charged rod close to the metal knob of the electroscope.
• The gold leaf (or aluminium foil) inside diverges, showing that the electroscope has acquired charge.
• Alternatively, a charged rod can attract small bits of paper, demonstrating the existence of an electrostatic force.

4. Conservation of Charge

The total electric charge of an isolated system remains constant. Charge can be transferred from one object to another, but it is never created or destroyed.

5. Units and Symbols

The SI unit of charge is the coulomb (symbol C). The symbol for charge is q (or Q for a total charge).

6. Quantisation of Charge

Charge occurs only in integer multiples of the elementary charge

\[

e = 1.602 \times 10^{-19}\,\text{C}.

\]

Thus any charge can be written as \(q = n e\) where \(n\) is an integer (positive, negative or zero).

7. Electric Field

An electric field \(\mathbf{E}\) exists in the region around a charged object. It is a vector quantity that tells us the force that would act on a test charge placed at any point in the field.

Direction definition: The direction of \(\mathbf{E}\) at a point is defined as the direction of the force that would act on a positive test charge placed at that point.

Mathematically

\[

\mathbf{E} = \frac{\mathbf{F}}{q_{\text{test}}},

\]

where \(\mathbf{F}\) is the force on a test charge \(q_{\text{test}}\) (taken as positive).

• If the test charge is positive, the force direction is the same as the field direction.
• If the test charge is negative, the force direction is opposite to the field direction.

8. Field‑Line Conventions (Cambridge syllabus)

• Field lines start on positive charges and end on negative charges.
• The tangent to a field line at any point gives the direction of \(\mathbf{E}\) there.
• Closer lines indicate a stronger field; farther apart lines indicate a weaker field.
• Field lines never cross.

Typical patterns

• Point charge (positive): Radial lines emerging straight outward from the charge.
• Point charge (negative): Radial lines converging inward toward the charge.
• Uniformly charged sphere (positive): Outside the sphere the field is identical to that of a point charge at the centre; inside a solid conductor the field is zero.
• Parallel‑plate capacitor (like charges on the plates): Straight, parallel lines from the positive plate to the negative plate, indicating a uniform field between the plates.

9. Worked Example (Numerical Check)

Problem: A point charge \(+5\,\mu\text{C}\) is placed at the origin. Find the magnitude and direction of the electric field at point \(P\) located \(0.10\,\text{m}\) to the right of the charge.

1. Use Coulomb’s constant \(k = 9.0 \times 10^{9}\,\text{N·m}^{2}\text{/C}^{2}\).
2. Calculate the magnitude:

   \[

   E = \frac{k\,|Q|}{r^{2}} = \frac{9.0 \times 10^{9}\times 5.0 \times 10^{-6}}{(0.10)^{2}}

   = 4.5 \times 10^{6}\,\text{N·C}^{-1}.

   \]

3. Direction: because the source charge is positive, the field points away from the charge. At point \(P\) the field points to the right (the + x direction).

Result: \(\mathbf{E}_{P}= 4.5 \times 10^{6}\,\text{N·C}^{-1}\) directed to the right.

10. Practical Tip for Laboratory Work

When handling charged objects, keep a metal part of your body (e.g., a wrist‑strap or a finger touching a grounded metal bench) to avoid accidental build‑up of static charge on yourself.

11. Summary

• The direction of the electric field at any point is the direction of the force on a positive test charge placed at that point.
• Friction generates charge by the transfer of electrons; the material that loses electrons becomes positively charged.
• Charge is conserved, quantised in units of \(e\), and measured in coulombs (C).
• Field‑line diagrams (point charge, charged sphere, parallel plates) visualise the direction and relative strength of \(\mathbf{E}\).
• Using \(\mathbf{E}= \mathbf{F}/q_{\text{test}}\) allows quick calculation of forces on any charge: \(\mathbf{F}=q\,\mathbf{E}\).