Describe an electric field as a region in which an electric charge experiences a force

Topic 4.2.1 – Electric Charge

Objective

Describe an electric field as a region in which an electric charge experiences a force, and use the concept in simple situations.

1. Electric charge

• Definition (syllabus wording): Charge is a fundamental property of matter that produces an electric force when the charged object is placed in an electric or magnetic field.
• Types of charge: positive (+) and negative (‑).
• Interaction: like charges repel, unlike charges attract.
• Quantisation: charge occurs in integer multiples of the elementary charge

  \[

  e = 1.602\times10^{-19}\ \text{C}

  \]

• Conservation of charge (syllabus wording): The total charge of an isolated system remains constant.

1.1 Producing electrostatic charge by friction (experiment)

1. Rub a dry glass rod vigorously with a piece of silk.
2. Electrons are transferred from the glass to the silk; the glass loses electrons and becomes positively charged, the silk gains electrons and becomes negatively charged.

1.2 Detecting static charge (experiments)

• Electroscope: A metal foil or leaf is mounted inside a glass jar and connected to a metal rod. When a charged object is brought near the rod, the leaf deflects away from the centre. The amount of deflection indicates the presence and relative magnitude of charge.
• Pith‑ball method: A lightweight pith‑ball is given a small charge and suspended from a thread. If a charged object is approached, the pith‑ball is attracted (opposite charges) or repelled (like charges), giving a quick visual test of the sign of the charge.

2. Units and symbols

Topic 4.2.2 – Electric Field

3. Electric field – definition (exact syllabus wording)

An electric field is a region of space surrounding one or more charges in which another electric charge would experience a force.

4. Direction of the field

• The direction of the field at any point is defined as the direction of the force that a positive test charge would feel there.
• If the source charge is positive the field points away from it; if the source charge is negative the field points toward it.

5. Visualising an electric field

• Field lines are a convenient way to show direction and relative magnitude.

  • Lines originate on positive charges and terminate on negative charges.
  • The density of lines (lines per unit area) indicates the strength of the field – more lines → stronger field.
  • Field lines never cross; at any point there is a single, well‑defined direction.

5.1 Field‑line patterns required by the Cambridge IGCSE syllabus

6. Electric field strength

At any point in a field the electric field strength is the force per unit positive test charge:

\[

E = \frac{F}{q}\qquad\text{(N C}^{-1}\text{)}

\]

Re‑arranged, the force on a charge \(q\) placed in a known field is:

\[

F = qE

\]

7. Field of a point charge

For a single point charge \(Q\), the magnitude of the electric field at a distance \(r\) is given by Coulomb’s law:

\[

E = \frac{1}{4\pi\varepsilon_{0}}\;\frac{|Q|}{r^{2}}

\qquad\text{where}\quad

\varepsilon_{0}=8.85\times10^{-12}\ \text{C}^{2}\text{N}^{-1}\text{m}^{-2}

\]

The direction is radial: away from a positive \(Q\) and toward a negative \(Q\).

8. Uniform field between parallel plates

• When two large, oppositely charged plates are placed close together, the field between them is approximately uniform.
• Field lines are straight, parallel to the plates and equally spaced; edge‑effects appear near the plate edges.
• Magnitude can be expressed as

  \[

  E = \frac{V}{d}

  \]

  where \(V\) is the potential difference and \(d\) the separation of the plates.

9. Conductors vs. insulators (experiment)

1. Charge a metal rod by rubbing it with a dry cloth (friction).
2. Suspend a small neutral aluminium foil piece from a thread.
3. Bring the charged metal rod close to the foil. The foil is attracted immediately because free electrons in the conductor move, producing an induced charge distribution (polarisation).
4. Repeat the test with a dry wooden stick (an insulator). The foil shows little or no attraction, demonstrating that charge cannot move freely in an insulator.

Result: Conductors allow free movement of charge; insulators do not.

10. Example problem (point charges)

Problem: Two point charges, \(+5\;\mu\text{C}\) and \(-3\;\mu\text{C}\), are 0.20 m apart. Find the magnitude and direction of the electric field at the midpoint.

1. Distance from each charge to the midpoint: \(r = 0.10\ \text{m}\).
2. Field due to \(+5\;\mu\text{C}\):

   \[

   E{+}= \frac{1}{4\pi\varepsilon{0}}\frac{5\times10^{-6}}{(0.10)^{2}}

   = 4.5\times10^{5}\ \text{N C}^{-1}

   \quad\text{(away from the + charge)}.

   \]

3. Field due to \(-3\;\mu\text{C}\):

   \[

   E{-}= \frac{1}{4\pi\varepsilon{0}}\frac{3\times10^{-6}}{(0.10)^{2}}

   = 2.7\times10^{5}\ \text{N C}^{-1}

   \quad\text{(toward the – charge)}.

   \]

4. Both fields point from the positive charge toward the negative charge, so they are in the same direction.

   \[

   E{\text{net}} = E{+}+E_{-}= 7.2\times10^{5}\ \text{N C}^{-1}.

   \]

5. Direction: From the \(+5\;\mu\text{C}\) charge toward the \(-3\;\mu\text{C}\) charge.

11. Key points to remember

• An electric field exists wherever a charge would experience a force.
• The field direction is defined by the force on a positive test charge.
• Field strength \(E\) is measured in N C⁻¹ (equivalently V m⁻¹).
• Field lines never intersect; a single direction is defined at every point.
• For multiple sources, the net field is the vector sum of the individual fields (superposition principle).
• Inside a charged conducting sphere the field is zero; outside it is radial and follows the point‑charge formula.
• Between large, oppositely charged parallel plates the field is approximately uniform and parallel to the plates.
• Conductors allow charge to move freely; insulators do not – demonstrated by the simple attraction experiment.

12. Practice questions

1. State the three fundamental properties of electric charge required by the Cambridge IGCSE syllabus.
2. A charge of \(+2\;\mu\text{C}\) creates an electric field of \(9.0\times10^{4}\ \text{N C}^{-1}\) at a point P. What force (magnitude and direction) does a test charge of \(-3\;\mu\text{C}\) experience at P?
3. Draw a qualitative field‑line diagram for:

   • a single positive point charge,
   • a uniformly charged conducting sphere,
   • two large oppositely charged parallel plates.

   Indicate on each diagram where the field strength is greatest.

4. Describe a simple experiment that can distinguish a conductor from an insulator using electrostatic charge.
5. Two equal positive charges are 0.15 m apart. At the point exactly midway between them, determine the direction of the net electric field and explain why the field magnitude is not zero.