Fields: Static vs. Changing, Uniform vs. Non-Uniform

Introduction to Fields

A field is a region of space where an object experiences a force. In VCE Physics, we consider gravitational, electric, and magnetic fields. Fields are used to explain action at a distance.

KEY TAKEAWAY: Fields are models that allow us to understand how objects interact without direct contact.

Static vs. Changing Fields

Fields can be classified as static or changing, based on whether their properties vary with time.

Static Fields

• A static field is constant in time. Its magnitude and direction at any given point in space remain the same.
• Examples:
  • Gravitational field due to a stationary mass.
  • Electric field due to stationary charges.
  • Magnetic field due to a permanent magnet at rest or a constant current in a stationary electromagnet.

Changing Fields

• A changing field varies with time. Its magnitude and/or direction at a given point in space changes.
• Examples:
  • Changing gravitational field (rare, but theoretically possible with accelerating large masses).
  • Electric field due to accelerating charges.
  • Magnetic field due to a moving magnet or a changing current in an electromagnet.

EXAM TIP: Be able to identify examples of static and changing fields in different contexts. Consider what causes the field and whether that source is changing over time.

Uniform vs. Non-Uniform Fields

Fields can also be classified based on their spatial uniformity.

Uniform Fields

• A uniform field has the same magnitude and direction at every point within the region of space being considered.
• Field lines are parallel and equally spaced.
• Examples:
  • Gravitational field near the Earth’s surface (over short distances).
  • Electric field between two large, parallel, oppositely charged plates.
  • Magnetic field inside a long solenoid (ideally).

Non-Uniform Fields

• A non-uniform field has a magnitude and/or direction that varies from point to point.
• Field lines are not parallel or equally spaced.
• Examples:
  • Gravitational field around a point mass (e.g., a planet).
  • Electric field around a point charge.
  • Magnetic field around a bar magnet.

Gravitational Field

• Uniform: Near the Earth’s surface, where $g$ is approximately constant (\$9.8 \, m/s^2$). Field lines are parallel and point downwards.
• Non-Uniform: Around a planet or any massive object. The field strength decreases with distance according to the inverse square law.

Electric Field

• Uniform: Between two parallel charged plates. Field lines are parallel and point from the positive plate to the negative plate.
• Non-Uniform: Around a point charge. The field strength decreases with distance according to the inverse square law. Field lines radiate outward from a positive charge and inward towards a negative charge.

Magnetic Field

• Uniform: Inside a long solenoid. Field lines are parallel and evenly spaced.
• Non-Uniform: Around a bar magnet. Field lines emerge from the north pole and enter the south pole.

COMMON MISTAKE: Confusing uniform and static. A field can be static but non-uniform (e.g., the gravitational field around a stationary planet). A field can also be changing and non-uniform (e.g., the electric field due to an accelerating charge).

Representing Fields with Field Lines

• Field lines are used to visualize the direction and strength of a field.
• The direction of the field line at any point indicates the direction of the force that a positive test charge (for electric fields) or a mass (for gravitational fields) would experience at that point.
• The density of the field lines (i.e., how close they are together) indicates the strength of the field. Closer lines mean a stronger field.
• Field lines never cross.

To represent vectors in three dimensions:

• Into the page: Represented by a cross (looks like the feathers of an arrow going away).
• Out of the page: Represented by a dot (looks like the tip of an arrow coming towards you).

(Diagram description: Illustration showing a cross representing a vector pointing into the page and a dot representing a vector pointing out of the page.)

STUDY HINT: Practice drawing field lines for different scenarios (point charges, parallel plates, magnets) to develop a strong understanding of field concepts.

Inverse Square Law

The magnitude of gravitational and electric fields around a point mass or charge follows an inverse square law. This means that the field strength is inversely proportional to the square of the distance from the source.

• Gravitational field: $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the object creating the field, and $r$ is the distance from the center of the object.
• Electric field: $E = \frac{kQ}{r^2}$, where $k$ is Coulomb’s constant, $Q$ is the charge creating the field, and $r$ is the distance from the charge.

APPLICATION: The inverse square law explains why the gravitational field is weaker further away from a planet, affecting satellite orbits and the trajectories of projectiles.

Potential Energy in Fields

The potential energy of an object in a field is related to the work done to move the object against the field force.

• Qualitative Analysis:
  • Moving a mass further away from another mass (against gravity) increases gravitational potential energy.
  • Moving a positive charge closer to another positive charge increases electric potential energy.
  • Moving a positive charge closer to a negative charge decreases electric potential energy.
• Uniform Gravitational Field: The change in gravitational potential energy is given by: $\Delta E_g = mg\Delta h$, where $m$ is the mass, $g$ is the gravitational field strength, and $\Delta h$ is the change in height.

VCAA FOCUS: Questions often involve determining whether potential energy increases or decreases as an object moves within a field. Remember to consider the direction of the force exerted by the field and the direction of the object’s displacement.