Electric Field: Force in Space

Lesson 3 of 5: Static Electricity

In this lesson:

• Why the electric field concept exists
• How to calculate the field from a point charge
• How to draw and read field line diagrams
• How to find force on a charge placed in a field

What You Will Learn in This Lesson

By the end, you will be able to:

1. Define the electric field and why it matters
2. Calculate electric field from a point charge
3. Determine field direction from source charge sign
4. Draw and interpret field line diagrams
5. Find force on a charge using

How Does One Charge Know Another Is There?

Coulomb's Law gives force between two specific charges.

But what happens in the space between them?

The charge creates a condition in space — the electric field — and anything placed in that space responds to it.

Electric Field Defined: Force per Unit Charge

The electric field at a point is the electric force per unit charge:

• = electric field (N/C)
• = force on a positive test charge
• The field exists in space regardless of whether is present

Electric Field of a Point Charge

• Involves one source charge (not two)
• Same inverse-square relationship as Coulomb's Law
• Coulomb: (two charges, gives force)
• Field: (one charge, gives field in space)

Direction of the Electric Field

Direction depends on the sign of the source charge:

• Positive source: field points away — positive test charge is repelled outward
• Negative source: field points toward — positive test charge is attracted inward

The field direction is defined for a positive test charge.

Worked Example: Step 1 — Find the Field

Given: A C charge at the origin. Find at m.

Direction: Source is positive → field points away from the charge, radially outward at m.

Worked Example: Step 2 — Find the Force

From Step 1: N/C pointing outward from the source.

Place a nC test charge at that point:

negative → force opposite to → toward the C source. Opposite charges attract ✓

Check: Which Formula Needs Two Charges?

Which formula requires two charges — and which requires only one?

• A) Coulomb's Law needs two; the field formula needs one
• B) Both formulas need two charges
• C) Both formulas need only one charge
• D) The field formula needs two; Coulomb's Law needs one

Formula Check: Answer and Explanation

A) Coulomb's Law needs two; field formula needs one

• — two charges interact
• — one source charge defines the field

Don't mix them up: is not a force — it's the field.

Bridge: From Formula to Field Line Diagrams

The formula gives the magnitude of at any point.

Field line diagrams show the field everywhere at once — direction and relative strength across the whole space.

Coming up: 5 rules for drawing field lines, then 4 key configurations.

Five Rules for Drawing Electric Field Lines

1. Lines originate on + charges; terminate on − charges (or → ∞)
2. Direction at any point = tangent to the field line
3. Density ∝ field strength — denser = stronger
4. Lines never cross — one field direction per point
5. Lines are perpendicular to conductor surfaces

Isolated Positive Charge: Field Lines Radiate Outward

• Lines point away from the positive charge in all directions
• Denser near the charge (stronger field) — spreads at distance

Isolated Negative Charge: Field Lines Point Inward

• Lines point toward the negative charge from all directions
• Same density pattern — denser near the charge

Dipole: Field Lines Curve from Plus to Minus

Field is strongest between the two charges — lines are most dense there.

Two Like Charges: Repelling Field Line Patterns

• Lines repel each other and curve outward
• Null point between the charges — field cancels to zero

Uniform Field: Evenly Spaced Parallel Lines

Between two parallel plates of opposite charge:

• Field lines are parallel and evenly spaced
• Uniform density → constant field strength everywhere between plates
• Field direction: from the positive plate toward the negative plate
• This is the standard lab setup for studying electric forces

Field Line Diagram Check: Finding the Errors

A student's diagram shows: (1) two field lines that cross each other; (2) field lines getting less dense closer to the charge; (3) a line that starts in empty space.

Which rule does each error violate?

Apply the 5 rules from Slide 11.

Field Line Error Check: Rules Identified

Error 1: Crossing lines → Rule 4 — one field direction per point

Error 2: Less dense near charge → Rule 3 — stronger field near charge; lines must be denser there

Error 3: Line starts in empty space → Rule 1 — lines originate only on charges

Bridge: Field Defined, Now Use It for Force

You know the electric field everywhere around a source charge.

When you place any charge in that field:

The sign of determines the direction of the force.

Force on a Charge in an Electric Field

• Positive : force in the same direction as
• Negative : force in the opposite direction to

The field direction is defined for a positive test charge — negative charges always respond oppositely.

Proton vs. Electron in Uniform Field

Same field — opposite force directions. Which accelerates more?

Worked Example: Force in a Uniform Field

Given: Uniform field N/C to the right.

Proton ( C):

Electron ( C):

Equal magnitude — opposite directions. Electron accelerates ~1836× more.

Direction Check: Negative Charge in a Field

Field points right. A charge of C is placed in it.

Which direction is the force?

• A) Right — same as the field
• B) Left — opposite to the field
• C) Zero — the charge cancels the field
• D) Upward — perpendicular to the field

Negative Charge Direction: Opposite to Field

B) To the left — opposite to the field

→ force is leftward

• Negative → force opposite to
• Option C is wrong: the charge responds to the field — it doesn't cancel it

Key Takeaways: Field Concept and Formula

✓ = force per unit charge — exists independently in space

✓ (one charge); Coulomb's Law uses two charges

✓ Positive source → away; negative source → toward

— use

Field lines show force direction — not paths

Key Takeaways: Field Lines and Force

✓ Field lines: originate on + charges, end on − charges, never cross

✓ Denser lines = stronger field — density is physical, not artistic

✓ : positive → with field; negative → against field

Negative charge: force opposite to — check 's sign

Coming Up: Electric Potential and Energy

Lesson 4 of 5: Electric Potential

• The energy stored in the arrangement of charges
• From force and field to potential
• Why understanding potential is essential for circuits

Prepare: understand that the field is a vector; potential is a scalar.