The Gravitational, Electric, and Magnetic Fields (HSC SSCE Physics): Revision Notes

The Gravitational, Electric, and Magnetic Fields

Understanding field models

Field models help us understand how forces can act between objects that aren't touching. This phenomenon is called force at a distance. You've now encountered three important field models in physics:

• Gravitational fields
• Electric fields (also called electrostatic fields)
• Magnetic fields

These three field models share some similarities but also have important differences that affect how they work.

Defining fields

All three types of fields can be described using the same mathematical relationship:

$\text{field} = \frac{\text{force}}{\text{property}}$

In this equation, property refers to the characteristic that both creates the field and experiences its effects.

Comparing the three field types

Each field type is created by a different property and acts on that same property.

Key points about field creation

• Gravitational fields are created by mass and affect other masses
• Electric fields are created by electric charge and affect other charges
• Magnetic fields are created by moving electric charges and affect other moving charges

Important differences between the fields

While all three fields follow the same basic definition, they behave quite differently in several important ways.

Motion requirements

One crucial difference is whether the object needs to be moving for the force to act:

Electric and gravitational forces affect particles whether they are stationary or moving. A charged particle feels an electric force and a massive object feels a gravitational force regardless of their motion.

Magnetic forces only affect charged particles that are moving relative to the magnetic field. If a charged particle is stationary, or if it's moving parallel to the magnetic field lines, it experiences no magnetic force at all.

Direction of forces

The three field types also differ in how their forces are oriented relative to the field lines:

Gravitational forces are always parallel to the gravitational field lines, pointing in the direction of the field (toward the mass creating it).

Electric forces are parallel to the electric field lines. The force can point either in the same direction as the field or opposite to it, depending on whether the charge is positive or negative. Either way, the force remains parallel to the field.

Magnetic forces are perpendicular to the magnetic field lines. A charged particle moving through a magnetic field experiences a force at right angles to both the field direction and its velocity. The specific direction is determined using the right-hand rule.

Particle paths in different fields

The different force directions lead to different types of motion:

In gravitational and electric fields, particles follow parabolic trajectories, similar to projectiles. The acceleration is constant in the direction of the field and zero perpendicular to it. This creates the familiar curved path of a projectile.

In magnetic fields, the motion is more complex:

• When a charged particle moves perpendicular to a uniform magnetic field, the perpendicular force causes it to travel in a circular path.
• If the particle's initial velocity has components both parallel and perpendicular to the field, it undergoes two types of motion simultaneously: circular motion in the plane perpendicular to the field, and constant velocity motion parallel to the field. This combination produces a helical path (like a spring or corkscrew).

Work and energy

Another key difference involves whether the field can do work on particles:

Gravitational and electric forces can do work when displacing a particle. As the particle moves through the field, its kinetic energy can change, with energy being transferred between the particle and the field.

Magnetic forces associated with a steady magnetic field cannot do work. This is because the magnetic force is always perpendicular to the particle's displacement. Since work requires a component of force in the direction of motion, and the magnetic force is always at right angles to the motion, no work is done.

The success and limitations of field models

Field models have been remarkably successful in explaining and predicting physical phenomena. The electric and magnetic field models form the foundation of electromagnetism, which describes a wide range of effects and underpins much of our modern technology.

However, field models cannot explain everything about the behaviour of charged particles such as electrons and protons. Scientists have developed an alternative approach called the quantum model or exchange particle model to explain interactions at the fundamental particle level.

The field model remains invaluable for explaining electric and magnetic phenomena and forms the basis of many technologies we use every day.