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# Properties of Electric Field Lines

## Key Concepts

• The importance of drawing electric field lines
• The properties of electric field lines
• The different patterns of electric field lines

## Introduction:

The strength of the electric field, E, at a location around a charge Q is determined with a small positive test charge q.  The direction of electric field strength depends upon the direction of force F acting on the positive test charge.

The concept of electric field lines was introduced by Michael Faraday to study the electric field strength and the direction of the electric field at different points around a charge.

A convenient way to study the electric field is to draw lines pointing in the direction of the electric field. This pattern of lines is known as electric field lines.

### Rules to draw electric field lines:

#### Rule-1

Field lines due to a positive charge:

In the case of a positive charge, the lines must begin on the positive charge and terminate at infinity.

Thus, the electric field lines are directed outward or away from a positive charge.

#### Rule-2

Field lines due to a negative charge: In the case of a negative charge, the lines must begin at infinity and terminate at the negative charge.

Thus, the electric field lines are directed inward or towards a negative charge.

#### Rule-3

The number of lines leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.

The object with a greater charge creates a stronger electric field. A strong electric field is represented with more lines. Thus, the strength of an electric field can be judged by the line density.

#### Rule-4

No two electric field lines from the same electric field can cross each other.

## Explanation:

### Properties of electric field lines:

• The electric field lines are imaginary lines, a visual representation of the electric field.
• The electric field lines from the same electric field never intersect with each other.
• The number of field lines gives the electric field strength of the electric field. The more the lines, the more the strength.
• The tangent drawn at a point to a field line gives the direction of the electric force acting on a unit positive test charge kept at that point in the electric field.
• The electric field lines are perpendicular to the surface of the charge.

### Electric field lines around different configurations of charges-1

The electric field lines for a positive charge are directed away from the charge because a positive test charge in this field would be repelled by the positive charge.

### Electric field lines around different configurations of charges-2

The electric field lines for a negative charge are directed towards the charge because a positive test charge in this field would be attracted by the negative charge.

### Electric field lines around different configurations of charges-3

The figure shows the electric field around two equal positive (and two equal negative charges) charges. The lines are radial and the same number of lines emerge from each charge because the charges are equal. At a greater distance from the charge, the field is approximately double (5+5 = 10C) of a single point charge of magnitude 5C.

### Electric field lines around different configurations of charges-4

The figure shows the electric field around two charges of equal magnitude but opposite signs. This charge configuration is called an electric dipole. At a point near the charge, the lines are radial and the number of lines leaving the positive charge equals the number of lines terminating on the negative charge.

### Electric field lines around different configurations of charges-5

The figure shows the electric field around two charges of different magnitude and signs. Here the number of lines originating from the positive charge is more than the number of lines terminating on the negative charge because the magnitude of the positive charge (+4C) is greater than the magnitude of the negative charge (-2C).

### Question: 1

Why do electric field lines originating from the same source never intersect?

The electric field around a charge has a unique magnitude and direction for a particular point in the space. A tangent drawn to an electric field line gives the direction of the electric field at that point.

If two electric field lines originating from the same source intersect then there would be two tangents and so two directions for the electric field at the same point, which is not possible. That is why electric field lines originating from a source never intersect.

### Question: 2

Whether the electric field lines form open curves or closed curves?

The electric field lines can never form closed loops, as lines can never start and end on the same charge. These field lines always start from the positive charge and terminate at the negative charge.

### Question: 3

Where is the electric field strength greater and where is weaker in the given figure?

The electric field strength is greater in the region “A” and ‘‘B’’ as in these regions the electric field lines are densely populated.

The electric field strength is weaker in the region “C” and “D” as in these regions the density of the electric field lines is very less.

### Question: 4

Where is the electric field uniform and where is the non-uniform in the given figure?

The electric field lines are uniform in region “A” as the electric field lines are equidistant here. The electric field lines are non-uniform in region “B” as here the electric field lines are not equidistant.

## SUMMARY

Electric Field Lines:

A convenient way to study the electric field is to draw lines pointing in the direction of the electric field. This pattern of lines is known as electric field lines.

• Properties of Electric Field Lines:
• The electric field lines for a positive charge are directed away from the charge because a positive test charge in this field would be repelled by the positive charge.
• The electric field lines for a negative charge are directed towards the charge because a positive test charge in this field would be attracted by the negative charge.
• The electric field lines are imaginal a visual representation of the electric field.
• The electric field lines from the same electric field never intersect with each other.
• The number of field lines gives the electric field strength of the electric field. The more the lines, the more the strength.
• The tangent drawn at a point to a field line gives the direction of the electric force acting on a unit positive test charge kept at that point in the electric field.
• The electric field lines are perpendicular to the surface of the charge.

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