Field Model Basics: Gravitation, Magnetism, and Electricity

Introduction to Fields

A field is a region of space where an object experiences a non-contact force. This model helps explain how objects interact without physically touching. VCE Physics focuses on three fundamental fields:

• Gravitational Fields: Associated with mass.
• Electric Fields: Associated with electric charge.
• Magnetic Fields: Associated with moving electric charges.

KEY TAKEAWAY: Fields are a model to explain forces acting at a distance.

Representing Fields

Fields are represented using field lines, which are imaginary lines that indicate the direction and strength of the field.

Characteristics of Field Lines

• Direction: Arrows on field lines indicate the direction of the force that a positive test particle (mass or charge) would experience.
• Strength: The density of field lines (how close they are together) indicates the strength of the field. Closer lines mean a stronger field; further apart lines mean a weaker field.
• Non-Intersection: Field lines never intersect. If they did, it would imply that the force at that point acts in two different directions simultaneously.
• Perpendicularity: Field lines meet surfaces perpendicularly.

EXAM TIP: When drawing field lines, always include arrows to indicate direction. Remember that field lines point in the direction a positive test charge would move.

Field Types

Fields can be classified as:

• Static vs. Changing:
  • Static Fields: Constant over time (e.g., a gravitational field due to a stationary mass, an electric field due to a stationary charge).
  • Changing Fields: Vary with time (e.g., electromagnetic waves).
• Uniform vs. Non-Uniform:
  • Uniform Fields: The field strength and direction are constant throughout the region (e.g., the electric field between two parallel charged plates). Field lines are parallel and equally spaced.
  • Non-Uniform Fields: The field strength and/or direction vary throughout the region (e.g., the gravitational field around a point mass).

COMMON MISTAKE: Confusing static/changing fields with uniform/non-uniform fields. They are independent classifications.

Gravitational Fields

• Source: Any object with mass.
• Direction: Always attractive, pointing towards the center of mass.
• Shape: Radially inwards for a point mass; parallel and downwards near the Earth’s surface (approximated as uniform).
• Monopole: Gravitational fields are considered monopoles because field lines always point towards the center of mass. There is no “negative mass” to create a repelling gravitational field.

Gravitational Field Strength

The gravitational field strength, $g$, is defined as the force per unit mass:

$$g = \frac{F_g}{m}$$

Where:

• $g$ is the gravitational field strength (N/kg or m/s²)
• $F_g$ is the gravitational force (N)
• $m$ is the mass (kg)

For a point mass $M$, the gravitational field strength at a distance $r$ is:

$$g = \frac{GM}{r^2}$$

Where:

• $G$ is the gravitational constant (\$6.674 \times 10^{-11} \, Nm^2/kg^2$)
• $M$ is the mass of the object creating the field (kg)
• $r$ is the distance from the center of the mass (m)

Gravitational Potential Energy

The gravitational potential energy, $E_g$, of an object with mass $m$ in a gravitational field is the energy it possesses due to its position in the field.

In a uniform gravitational field (near the Earth’s surface), the change in gravitational potential energy is:

$$E_g = mg\Delta h$$

Where:

• $m$ is the mass (kg)
• $g$ is the gravitational field strength (N/kg)
• $\Delta h$ is the change in height (m)

STUDY HINT: Remember that gravitational potential energy is relative. We often set the zero point at the Earth’s surface.

Electric Fields

• Source: Electric charge (positive or negative).
• Direction:
  • Away from positive charges.
  • Towards negative charges.
• Shape: Radially outwards from a positive point charge; radially inwards towards a negative point charge; uniform between parallel charged plates.
• Dipole: Electric fields can be monopoles (single positive or negative charge) or dipoles (two equal and opposite charges).

Electric Field Strength

The electric field strength, $E$, is defined as the force per unit positive charge:

$$E = \frac{F}{q}$$

Where:

• $E$ is the electric field strength (N/C or V/m)
• $F$ is the electric force (N)
• $q$ is the charge (C)

For a point charge $Q$, the electric field strength at a distance $r$ is:

$$E = \frac{kQ}{r^2}$$

Where:

• $k$ is Coulomb’s constant (\$8.988 \times 10^9 \, Nm^2/C^2$)
• $Q$ is the charge creating the field (C)
• $r$ is the distance from the charge (m)

Between parallel plates with a voltage $V$ and separation $d$, the uniform electric field strength is:

$$E = \frac{V}{d}$$

Electric Potential Energy

The electric potential energy, $E_e$, of a charge $q$ in an electric field is the energy it possesses due to its position in the field.

The work done, $W$, to move a charge $q$ through a potential difference $V$ is:

$$W = qV$$

In a uniform electric field: $V = Ed$, so $W=qEd$.

REMEMBER: “Positive charges follow the field, negative charges go against it”. Positive charges gain kinetic energy when moving in the direction of the electric field, while negative charges gain kinetic energy when moving against the field.

Magnetic Fields

• Source: Moving electric charges (electric current).
• Direction: Determined by the right-hand rule.
• Shape:
  • Around a straight current-carrying wire: concentric circles.
  • Inside a solenoid: approximately uniform.
  • Around a bar magnet: from the north pole to the south pole outside the magnet, and from the south pole to the north pole inside the magnet.
• Dipole: Magnetic fields are always dipoles. Isolated magnetic monopoles (north or south) have not been observed.

Magnetic Field Lines

• Field lines emerge from the north pole of a magnet and enter the south pole.
• Inside the magnet, field lines continue from the south pole to the north pole, forming closed loops.

Magnetic Field Strength

The magnetic field strength is represented by the symbol $B$ and is measured in Tesla (T). The calculation of $B$ depends on the source of the magnetic field (e.g., current in a wire, solenoid). These calculations are covered in more detail in later sections.

APPLICATION: Magnetic fields are used in electric motors to generate torque and cause rotation.

Comparing Gravitational, Electric, and Magnetic Fields

VCAA FOCUS: VCAA often asks students to compare and contrast these three fields, focusing on their sources, directions, and the types of objects they affect.