Part 2 of the fields saga.

• Field lines
• Uniform vs radial fields
• Superposition of Fields

---

How else can we represent forces in a field?
It is more intuitive to use a bunch of arrows (of different lengths and directions) to represent field strength at different points in space.

However, it is simply too difficult to draw on paper. Besides, it gets very messy when you try to draw too many arrows.

We can draw the direction of forces as FIELD LINES.

These are basically just lines with a direction that connect the small vectors (arrows) on each point in a field.

If our vector field looks like this:

The same field using field lines looks like this:

These lines show the direction forces act in a field.

We can represent the strength of a field (how large the force is at any point) by HOW CLOSE the field lines are together. The more field lines you have, the stronger the field.

Stronger field
Weaker field

---

Field Shapes
Field lines can be arranged in different ways depending on the nature of the field. Here are the 2 most common types of simple fields & their properties:

Radial fields	– field lines (seem to) emanate from a single point – no field lines intersect – drawing a circle centred on the point of origin, field lines are always perpendicular to the surface of that circle – field strength decreases as you travel further from the origin
Uniform fields	– field lines are parallel – no field lines intersect – field lines are always perpendicular to the surface that they emanate from – field strength remains constant at all distances

Since the field strength is represented by how close the field lines are at any point, you know that field strength decreases if the field lines diverge. Uniform fields have uniform field strength, so you see that their field lines don’t get closer or further away – they remain parallel!

---

Superposition of Fields
Principle of Superposition:

• When several forces act on an object, the resultant force is the vector sum of all the forces. This complies with Coulomb’s Law and Newton’s Law of Gravitation
• If the (gravitational/electric) field at a point in space is due to more than one (mass/charge), the total field at that point = vector addition of each individual field caused by each (mass/charge)

Let’s try this in an Electric Field:

Find the resultant Electric Field at many points in space:

Using the field line representation, you get this familiar picture:

You can try to “derive” the field line representation when there is one positive charge and one negative charge. Just repeat the process: use the principle of superposition to find the resultant fields at a number of points!

Why don’t field lines intersect?
If field lines intersect, it means that at the point of intersection, the (mass/charge) can move in two directions! This is not true. We already use field lines to show the RESULTANT force on the object, so you can’t accelerate in 2 different directions.

---

Special thanks to my friend Tian Ern for helping with the drawings! I need to get a tablet one day…

---