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:

Gravitational fieldThis image has an empty alt attribute; its file name is quackpotential.pngWork is done on the duck
Electric fieldThis image has an empty alt attribute; its file name is chargepotential.pngWork is done on the charge

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.

The shark has more potential energy due to its higher mass, so it will gain a higher kinetic energy once it reaches a ground. If a shark hits you on the head, it would hurt more than a duck.

We call positions with constant potential as EQUIPOTENTIAL.

Dotted lines are usually used to represent equipotential lines

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.

Gravitational force causes duck to accelerate from a high potential to a lower potential

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!

The red ball has 0 horizontal velocity, which it maintains throughout its journey, but it accelerates downwards vertically. The blue ball has a horizontal velocity, but it also maintains that component – it only accelerates vertically downwards.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s