# Concept of Electric field lines

Let us now learn about field lines which are a pictorial representation or way to imagine electric fields. The notion of the electrical field was first presented by the 19th-century physicist Michael Faraday. It was Faraday's understanding that the pattern of lines describing the electric field is an invisible reality.

For a single positive point charge q, the electric field is given by relation

$\vec{F}=\frac{kq{\widehat{r}}}{4\pi \epsilon _{0}r^{2}}$

now to get a feel of this field one can sketch a few representative vectors as shown in fig below

• Since the electric field varies as the inverse of the square of the distance that points from the charge the vector gets shorter as you go away from the origin and they always point radially outwards.
• Connecting up these vectors to form a line is a nice way to represent the electric field.
• An electric field line is an imaginary line drawn in such a way that its direction at any point is the same as the direction of the field at that point.
• Field-line in general is a curve drawn in such a way that the tangent to it at each point in the direction of the net field at that point.

### Concept and Definition

Definition: An electric field line is an imaginary line or curve drawn over an empty space region such that its tangent at each position, points in the direction of the electric field vector at this position.

The relative spacing between lines provides an indication of the electric field strength at that point. So,

• The magnitude of the field is indicated by the density of the lines. This means that electric field strength due to the charged body is more in the region where the density of field lines is high. In the region where the density of these lines is low, the electric field has lower strength.
• Magnitude is strong near the center where the electric field lines are close together, and it becomes weak as ve move farther outwards, where they are relatively apart or they have less density.
• A field line or electric line of force can be considered as the path along which a small positive test charge would move if we let it move freely along the path.

## Rules for Drawing Electric Field lines Patterns

1. The field line begins at the +ive charge and ends either at the -ive charge or at infinity. So we can draw electric field vectors at each point in space around the charge and join them to form the lines.
2. It must be noted that for each location, the electric field vectors point tangent to the direction of the electric field lines at any given point. (physicsclassroom.com)
3. When the field is stronger, the field lines are closer to each other.
4. The number of field lines depends on the magnitude of the electric charge.
5. The field lines should never cross each other.

## Field Lines due to some charge configurations

### For a positive charge

• Field lines of a single +ive charge point radially outwards

### For a negative charge

• For a negative charge, they are radially inwards as shown below in the figure

These two figure given above shows how to draw field lines for a single charge (+ive and -ive)

### Electric Field Lines for Configurations of Two or More Charges

• Field lines around the system of two +ive charges give a different picture and describe the mutual repulsion between them.

• Field lines around a system of a positive and -ive charge clearly show the mutual attraction between them as shown below in the figure.

## Properties Of Electric Field Lines

Some important general properties of field lines are

1. Field lines start from a positive charge and end on a negative charge.
2. They are directed away from the positive electric charge and towards the negative electric charge. So, at any point tangent to field lines give the direction of the electric field at that point.
3. These lines leave or enter the charged surface normally.
4. Field lines never cross each other because if they do so then at the point of intersection there will be two directions of the electric field.
5. Electric field lines do not pass through a conductor, this shows that the electric field inside a conductor is always zero.
6. Electric field lines are continuous curves in a charge-free region.
7. Electric field lines have the tendency to contract in length. This explains the existence of the electric force of attraction between two oppositely charged objects.
8. Electric lines of force have a tendency to expand laterally, i.e., they tend to separate from each other in the direction perpendicular to their lengths. This explains the electric force of repulsion between like charges.

### Questions

What does an electric field line represent?
When are electric field lines parallel to each other?
Where do electric field lines start and end?