Physics (9702)
Topic 10 of 17Cambridge A Levels

Electric Fields

The region around a charge where another charge experiences an electrostatic force.

### Introduction to Fields

In physics, a field is a region of space in which an object experiences a force due to a particular property. For example, a mass creates a gravitational field around it. Similarly, an electric charge creates an electric field in the space surrounding it. This field is the medium through which electric forces are exerted. We can define an electric field as a region of space where a stationary electric charge experiences an electrostatic force.


### Coulomb's Law

The fundamental law governing the interaction between stationary electric charges is Coulomb's Law. It states that the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between their centres.


Mathematically, this is expressed as:

F = (1 / 4πε₀) * |q₁q₂| / r²


Where:

  • F is the magnitude of the electrostatic force in Newtons (N).
  • q₁ and q₂ are the magnitudes of the two point charges in Coulombs (C).
  • r is the distance between the centres of the charges in metres (m).
  • ε₀ is the permittivity of free space, a fundamental constant with a value of approximately 8.85 x 10⁻¹² F m⁻¹.
  • The term (1 / 4πε₀) is often simplified as Coulomb's constant, k ≈ 8.99 x 10⁹ N m² C⁻².

    • This is an inverse square law, meaning the force decreases rapidly as the distance increases. The force is a vector: it is repulsive for like charges (both positive or both negative) and attractive for opposite charges (one positive, one negative).


    ### Electric Field Strength (E)

    While Coulomb's Law describes the force between two specific charges, electric field strength (E) describes the effect of a source charge on the space around it. It is defined as the electrostatic force experienced per unit positive test charge placed at a point in the field.


    The formula is:

    E = F / q


    Where q is a small, positive test charge that is used to probe the field without significantly disturbing it. The unit for electric field strength is Newtons per Coulomb (N C⁻¹). It is also equivalent to Volts per metre (V m⁻¹), a unit you will encounter when studying electric potential.


    Since E is based on the force F, it is also a vector quantity. Its direction is defined as the direction of the force that would be exerted on a positive test charge. Therefore, electric field lines point away from positive charges and towards negative charges.


    We can derive the formula for the electric field strength due to a single point charge, Q, by combining the two equations above:

    E = ( (1 / 4πε₀) * |Qq| / r² ) / q

    This simplifies to:

    E = (1 / 4πε₀) * Q / r²

    This formula allows us to calculate the strength of the field at any distance r from a source charge Q.


    ### Representing Electric Fields

    Electric fields are visualized using electric field lines (or lines of force). These lines follow specific rules:

  • They originate on positive charges and terminate on negative charges (or extend to infinity).
  • The tangent to a field line at any point gives the direction of the electric field vector E at that point.
  • The density of the lines (how close they are to each other) is proportional to the magnitude of the electric field strength. Closer lines indicate a stronger field.
  • Field lines can never cross.

    • ### Electric Potential (V)

    Just as a mass in a gravitational field has gravitational potential energy, a charge in an electric field has electric potential energy. From this, we derive the concept of electric potential (V). It is defined as the work done per unit positive charge in moving a charge from infinity to a point in the electric field.


    V = W / q


    Where W is the work done (in Joules) and q is the charge (in Coulombs). The unit of electric potential is the Volt (V), which is equivalent to a Joule per Coulomb (J C⁻¹).


    Unlike electric field strength, electric potential is a scalar quantity. However, it does have a sign. The potential is positive at a point if work is done against the field to bring a positive charge there (i.e., near a source positive charge). It is negative if work is done by the field (i.e., near a source negative charge).


    The formula for the electric potential at a distance r from a point charge Q is:

    V = (1 / 4πε₀) * Q / r


    Notice this is not an inverse square relationship; potential is inversely proportional to r, not r². The potential difference between two points is the work done in moving a unit positive charge from one point to the other.

    Key Points to Remember

    • 1An **electric field** is a region of space where a charge experiences an electrostatic force.
    • 2**Coulomb's Law (F ∝ q₁q₂ / r²)** quantifies the inverse-square force between two point charges.
    • 3**Electric field strength (E = F/q)** is the force per unit positive charge at a point; it is a vector quantity measured in N C⁻¹.
    • 4The electric field strength due to a point charge Q is given by **E = (1 / 4πε₀) * Q / r²**.
    • 5**Electric potential (V = W/q)** is the work done per unit charge to move it from infinity to a point; it is a scalar quantity measured in Volts (V).
    • 6The electric potential due to a point charge Q is given by **V = (1 / 4πε₀) * Q / r**.
    • 7Electric field lines show the direction (tangent) and strength (density) of the field, pointing away from positive and towards negative charges.
    • 8Potential is positive around a positive source charge and negative around a negative source charge.

    Pakistan Example

    Controlling Air Pollution with Electric Fields in Pakistani Industries

    Cement plants and power stations in Pakistan, such as the Lucky Cement plant near Karachi or thermal power plants in Punjab, use **electrostatic precipitators**. These devices create a strong electric field. As smoke and dust particles pass through, they become negatively charged. Positively charged collection plates then attract these particles using the electrostatic force (**F = qE**), removing them from the exhaust gases and preventing them from polluting the atmosphere. This is a direct, large-scale application of Coulomb's law and electric field principles to solve a major environmental problem.

    Quick Revision Infographic

    Physics — Quick Revision

    Electric Fields

    Key Concepts

    1An **electric field** is a region of space where a charge experiences an electrostatic force.
    2**Coulomb's Law (F ∝ q₁q₂ / r²)** quantifies the inverse-square force between two point charges.
    3**Electric field strength (E = F/q)** is the force per unit positive charge at a point; it is a vector quantity measured in N C⁻¹.
    4The electric field strength due to a point charge Q is given by **E = (1 / 4πε₀) * Q / r²**.
    5**Electric potential (V = W/q)** is the work done per unit charge to move it from infinity to a point; it is a scalar quantity measured in Volts (V).
    6The electric potential due to a point charge Q is given by **V = (1 / 4πε₀) * Q / r**.

    Formulas to Know

    Electric field strength (E = F/q)** is the force per unit positive charge at a point; it is a vector quantity measured in N C⁻¹.
    Q is given by **E = (1 / 4πε₀) * Q / r²**.
    Electric potential (V = W/q)** is the work done per unit charge to move it from infinity to a point; it is a scalar quantity measured in Volts (V).
    Q is given by **V = (1 / 4πε₀) * Q / r**.
    Pakistan Example

    Controlling Air Pollution with Electric Fields in Pakistani Industries

    Cement plants and power stations in Pakistan, such as the Lucky Cement plant near Karachi or thermal power plants in Punjab, use **electrostatic precipitators**. These devices create a strong electric field. As smoke and dust particles pass through, they become negatively charged. Positively charged collection plates then attract these particles using the electrostatic force (**F = qE**), removing them from the exhaust gases and preventing them from polluting the atmosphere. This is a direct, large-scale application of Coulomb's law and electric field principles to solve a major environmental problem.

    SeekhoAsaan.com — Free RevisionElectric Fields Infographic

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