# PHY: Fields & Energy

The final entry of the fields trilogy:

• Field Potential Energy
• Field Potential
• How forces arise through potential differences

Let’s jump in!

How do fields relate to energy?
Objects in any position in a field possess POTENTIAL ENERGY.

Why?
Let’s look at a falling duck:

When the duck is at this position in Earth’s gravitational field, it can fall and gain kinetic energy. It gains kinetic energy because there is a force acting on it due to the field. However, this energy must come from somewhere – it cannot be created from nothing! So we call this initial energy ‘POTENTIAL ENERGY’.

An object in a field can convert some of that potential energy into other forms of energy. We define a transformation of energy as work. Objects in a field have the ability to do work – thus, they have ENERGY.

Forces in fields can do work on objects. Here are a few examples:

How does potential energy change as you move through a field?
It decreases as you follow the field lines, and increases as you go against them.

Imagine that duck again. If the duck travels along the gravitational field lines like so:

The duck LOSES gravitational potential energy. It has less energy to convert into other forms, so it can do less work. If a duck drops onto your head from a lower height, it would hurt a lot less.

If the duck travels against the gravitational field lines like so:

The duck GAINS gravitational potential energy. It has more energy to convert into other forms, so it can do more work. If a duck drops onto your head from a higher height, it would hurt a lot more.

How does the duck move against the field? You need to do WORK AGAINST the field. For example, the duck needs to flap its wings to exert a lifting force and travel upwards. It does work against the gravitational field.

What is potential?
Potential energy per unit property (which interacts with the field).

For example:

• gravitational potential is gravitational potential energy per unit mass
• electric potential is electric potential energy per unit electric charge

This is handy when we are dealing with multiple objects with different values in the same field. A 100kg shark and 1kg duck at the same height above the Earth have the same potential, but different potential energies.

We call positions with constant potential as EQUIPOTENTIAL.

How are forces related to potential & potential energy?
Since objects in a field have potential energy, they have the ability to do work by moving – more specifically, ACCELERATING.

Objects tend to change their position from a high potential to a low one. If you place a mass at a position with high gravitational potential, it starts to accelerate “downwards” towards a position with lower potential. The cause of this mysterious acceleration is what we label as a FORCE. In fact, this is how forces arise – they stem from differences in potential between 2 points.

This is why objects moving across an equipotential will do so at a constant velocity in the direction of the equipotential. For example, a ball thrown horizontally in a gravitational field will accelerate vertically downwards, but there is no horizontal acceleration!