Basics of Electric Fields

Representing an Electric Field

An electric field exists around any charged object. If another charged object is placed in this field, it experiences an electric force.

Electric fields are invisible, so physicists use electric field lines to represent them.

Field lines help us visualize two important properties of an electric field:

• The direction of the field
• The relative strength of the field

The lines themselves are not physical objects. They are a model that helps us understand how a charge would behave at different positions in the field.

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Direction of Electric Field Lines

The direction of an electric field is defined as the direction in which a positive test charge would experience a force.

This gives us a simple rule:

Electric field lines point away from positive charges and toward negative charges.

For a positive charge:

Positive charge → field points outward

For a negative charge:

Negative charge → field points inward

This convention applies even if the particle actually placed in the field is negatively charged.

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Field Lines Around a Positive Charge

An isolated positive point charge produces a field that extends outward in all directions.

The field has radial symmetry.

This means that the field pattern looks the same in every direction around the charge.

In a sketch:

• Place the positive charge at the centre.
• Draw several lines extending outward.
• Put arrowheads pointing away from the charge.
• Spread the lines evenly around the charge.

As the distance from the charge increases, the electric field becomes weaker.

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Field Lines Around a Negative Charge

An isolated negative point charge also produces a field with radial symmetry.

The important difference is the direction.

In a sketch:

• Place the negative charge at the centre.
• Draw several lines approaching the charge from different directions.
• Put arrowheads pointing toward the charge.
• Spread the lines evenly around the charge.

The field becomes stronger as you approach the charge.

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Field Line Density and Field Strength

Electric field diagrams can also provide information about field strength.

The general rule is:

Closer field lines → stronger electric field

More widely spaced field lines → weaker electric field

This is sometimes described in terms of field line density.

A region containing many field lines close together represents a stronger electric field than a region where the lines are more widely separated.

The number of drawn lines is a convention of the diagram; what matters when interpreting a given diagram is their relative spacing or density.

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Why the Field Weakens with Distance

Around an isolated point charge, the field lines spread farther apart as the distance from the charge increases.

This represents the fact that electric field strength decreases with distance.

For a point charge, the relationship is:

\( E \ \alpha \ \frac{1}{r^2} \)

This means electric field strength follows an inverse-square relationship.

If the distance from the charge doubles:

\( E_{\text{new}} = \frac{E}{4} \)

If the distance triples:

\( E_{\text{new}} = \frac{E}{9} \)

The increasingly wide spacing of field lines provides a visual representation of this decreasing field strength.

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Reading a Field Diagram

When you are given an electric field diagram, ask two questions.

Which way does the field point?

Look at the arrowheads on the field lines.

Where is the field strongest?

Look for the region where the field lines are most densely packed.

For example, if the lines are tightly packed near a charge and spread farther apart with distance, the field is stronger near the charge and weaker farther away.

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Worked Example: Comparing Two Locations

Imagine two points, A and B, near a positive charge.

Point A is close to the charge.

Point B is much farther away.

At Point A, the field lines are relatively close together.

At Point B, the lines are farther apart.

Therefore:

Electric field at A > Electric field at B

A positive test charge placed at A would experience a greater force than the same test charge placed at B.

This follows from:

\( F = qE \)

For the same test charge

$q$

, a larger field strength

$E$

produces a larger electric force.

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Field Lines Between Opposite Charges

Consider a positive charge placed near a negative charge.

Field lines begin at the positive charge and end at the negative charge.

Therefore:

Positive → Negative

The lines curve because the total electric field at each point is produced by both charges.

This arrangement of equal and opposite charges is called an electric dipole.

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Understanding the Dipole Pattern

Near the positive charge, the field points generally away from the positive charge.

Near the negative charge, the field points generally toward the negative charge.

Between the two charges, these effects reinforce each other.

A positive test charge placed between the charges would:

• be repelled by the positive charge
• be attracted toward the negative charge

Both forces act generally from the positive charge toward the negative charge.

The electric field between the charges can therefore be relatively strong.

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Field Lines Between Two Positive Charges

Now consider two positive charges.

Both charges produce fields pointing outward.

Between the charges:

• the left positive charge produces a field pointing away from itself
• the right positive charge also produces a field pointing away from itself

The two fields therefore oppose each other in the region between the charges.

For two identical positive charges, there is a point exactly halfway between them where the two electric fields have equal magnitudes and opposite directions.

At that point:

\( E_{\text{net}} = 0 \)

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Field Lines Between Two Negative Charges

Two negative charges produce a similar overall pattern, but the field lines point toward the charges.

For two identical negative charges, the fields at the midpoint are equal in magnitude and opposite in direction.

Therefore, at the exact midpoint:

\( E_{\text{net}} = 0 \)

The field is zero at that single point even though strong electric fields exist nearby.

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Electric Field Lines Never Cross

An important rule is:

Electric field lines never cross.

Why?

At any particular point in space, the electric field has only one net direction.

If two field lines crossed, the crossing point would suggest that the electric field had two different directions at the same location.

That is impossible.

Therefore, correctly drawn electric field lines cannot cross.

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Field Lines Do Not Suddenly Stop in Empty Space

Electric field lines generally:

• begin on positive charges and end on negative charges, or
• extend to or from very large distances when the appropriate opposite charge is not shown

They should not simply stop in empty space without a physical reason.

This rule helps identify incorrectly drawn field diagrams.

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Field Lines and Electric Force

The direction of a field line tells us the direction of force on a positive test charge.

Therefore:

Positive charge → force in the same direction as the field

However, a negative charge experiences force in the opposite direction.

Therefore:

Negative charge → force opposite to the field direction

For example, suppose the electric field points to the right.

A positive charge experiences a force to the right.

A negative charge experiences a force to the left.

This follows from:

\( \vec{F} = q\vec{E} \)

The negative value of

$q$

reverses the direction of the force.

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Worked Example: Reading Force from a Field Diagram

Suppose a field diagram shows field lines pointing from left to right.

A positive charge is placed in the field.

Its force will point:

to the right

Now replace it with a negative charge.

Its force will point:

to the left

The electric field itself has not changed.

Only the direction of the force on the test charge has changed.

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Comparing Field Strengths

Suppose a field diagram contains three locations: A, B, and C.

At A, the field lines are tightly packed.

At B, they are moderately spaced.

At C, they are widely spaced.

The relative field strengths are:

A strongest

B intermediate

C weakest

You do not necessarily need numerical values to make this comparison.

The field-line pattern itself provides information about relative field strength.

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Uniform Electric Fields

Not all electric fields spread outward from point charges.

A nearly uniform electric field can exist between two large, oppositely charged parallel plates.

In a uniform field:

• field lines are straight
• field lines are parallel
• field lines are approximately equally spaced
• field direction is the same throughout the central region
• field strength is approximately constant throughout that region

The lines point from the positive plate toward the negative plate.

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Uniform vs. Non-Uniform Fields

A uniform electric field has approximately the same magnitude and direction throughout a region.

It can be represented by:

• parallel field lines
• equal spacing between lines

A non-uniform electric field changes with position.

The field around a point charge is non-uniform because:

• its direction changes depending on position
• its strength decreases with distance

The field lines therefore spread apart as they move away from the charge.

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Sketching Electric Field Patterns

When drawing electric field diagrams, follow these rules:

• Draw arrows away from positive charges.
• Draw arrows toward negative charges.
• Use closer line spacing to represent stronger fields.
• Use wider line spacing to represent weaker fields.
• Never allow field lines to cross.
• For isolated point charges, use a symmetrical radial pattern.
• For interacting charges, allow the lines to curve according to the combined field.
• For uniform fields, draw straight, parallel, equally spaced lines.

The goal is not simply to create a neat picture. The diagram should communicate the direction and relative strength of the electric field.

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Sketching an Isolated Positive Charge

Start by drawing:

( + )

Draw lines radiating outward in several directions.

Add arrowheads pointing away from the charge.

Keep the pattern symmetrical.

This represents the field produced by an isolated positive point charge.

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Sketching an Isolated Negative Charge

Start with:

( − )

Draw radial lines surrounding the charge.

Place the arrowheads pointing toward the charge.

Again, keep the pattern symmetrical.

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Sketching Opposite Charges

Start with:

( + ) ( − )

Draw field lines beginning at the positive charge and ending at the negative charge.

The lines between the charges should point:

+ → −

Additional lines should curve around the outside while still travelling from the positive charge toward the negative charge.

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Sketching Two Like Charges

For two positive charges:

( + ) ( + )

Field lines leave both charges.

Between the charges, the fields oppose each other.

The lines bend away from the central region rather than joining one positive charge to the other.

For equal charges, the exact midpoint is a zero-field point.

For two negative charges, the pattern has a similar shape, but the arrows point inward toward the charges.

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Principle of Superposition

When several charges are present, each charge produces its own electric field.

The actual electric field at a point is the vector sum of all these fields.

This is called the principle of superposition.

In one dimension:

\( E_{\text{net}} = E_1 + E_2 + E_3 + \cdots \)

Direction must be considered.

For example:

Field from Charge A = 700 N/C right

Field from Charge B = 300 N/C left

Choose right as positive:

\( E_{\text{net}} = +700 - 300 = +400\text{ N/C} \)

Therefore, the net electric field is 400 N/C to the right.

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Field Lines as a Model

Field lines are extremely useful, but they are only a model.

There are not actual lines floating through space around a charged object.

A diagram might show 8, 12, or 20 lines around a charge, but the electric field exists throughout the surrounding region, not only along those drawn lines.

Field lines allow us to visualize:

• direction
• relative strength
• symmetry
• interactions between fields

The number of lines drawn is chosen to make the diagram useful and readable.

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Common Mistakes

Drawing Field Lines Toward Positive Charges

Remember:

Positive → field lines point away

Negative → field lines point toward

Thinking Field Lines Are Physical Objects

Field lines are a visual model of an electric field.

Allowing Field Lines to Cross

Field lines cannot cross because the net electric field cannot have two different directions at the same point.

Ignoring Line Spacing

Field line density provides information about field strength.

Closer lines = stronger field

Wider spacing = weaker field

Assuming a Negative Charge Moves in the Direction of the Field

The field direction is defined using a positive test charge.

A negative charge experiences a force opposite to the field direction.

Connecting Two Positive Charges with Field Lines

Field lines do not normally begin on one positive charge and end on another positive charge.

They point away from both positive charges.

Assuming Zero Field Means No Fields Are Present

At a cancellation point, several electric fields may be present but their vector sum is zero.

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Check Your Understanding

1. What information do electric field lines provide?

2. In which direction do field lines point around a positive charge?

3. In which direction do field lines point around a negative charge?

4. What does closely spaced field-line density indicate?

5. Why do field lines spread farther apart with increasing distance from an isolated point charge?

6. Why can electric field lines never cross?

7. Describe the field pattern around an isolated positive point charge.

8. Describe the field pattern around an isolated negative point charge.

9. In which direction do field lines travel between a positive and negative charge?

10. What happens to the electric fields at the exact midpoint between two identical positive charges?

11. How would you identify the strongest region in a field-line diagram?

12. Describe the field-line pattern in a uniform electric field.

13. A field points right. In which direction would a positive charge experience a force?

14. A field points right. In which direction would a negative charge experience a force?

15. Explain why field lines are considered a model rather than physical objects.

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Key Terms

• Electric field – a region in which a charged object experiences an electric force.
• Electric field line – a line used to represent the direction and relative strength of an electric field.
• Field direction – the direction in which a positive test charge would experience a force.
• Field strength – the force per unit positive charge at a particular point.
• Field line density – the relative closeness of field lines used to represent field strength.
• Radial field – a field whose lines extend directly toward or away from a central point.
• Uniform electric field – a field with approximately constant magnitude and direction throughout a region.
• Non-uniform electric field – a field whose magnitude or direction changes with position.
• Electric dipole – a pair of opposite charges separated by a distance.
• Superposition – the principle that electric fields from different charges combine through vector addition.
• Test charge – a small positive charge used conceptually to determine field direction.

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Key Takeaways

• Electric field lines provide a visual representation of electric field direction and relative strength.
• Field lines point away from positive charges.
• Field lines point toward negative charges.
• The electric field is stronger where field lines are more densely packed.
• The electric field is weaker where field lines are more widely spaced.
• Field lines around isolated point charges form radial patterns.
• Field lines between opposite charges travel from the positive charge toward the negative charge.
• Field lines around like charges bend away from the region between the charges.
• Electric field lines never cross.
• A uniform electric field is represented by parallel, equally spaced field lines.
• Field diagrams can be used to compare electric field strengths without knowing numerical values.
• Field lines are a model; they are not physical structures in space.