Topic 10.213 min read
Electric Field Intensity
Electric field intensity at a point is the electrostatic force per unit positive test charge placed at that point. It is a vector, written as E⃗=F⃗/q. For a point source charge Q, its magnitude is E=k|Q|/r², and its direction is away from a positive source or toward a negative source.
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The main idea
A charged object changes the space around it. Another charge placed in this region feels an electric force. We describe the strength and direction of that effect using electric field intensity.
- \vec E
- electric field intensity (N·C⁻¹)
- \vec F
- force on a positive test charge (N)
- q
- magnitude of the positive test charge (C)
Direction around a point charge
- Positive source charge: field points radially outward.
- Negative source charge: field points radially inward.
- Larger source charge: stronger field at the same distance.
- Greater distance: weaker field because E∝1r².
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Meaning of an electric field
An electric field is a vector field surrounding a charged object. It tells us the magnitude and direction of the electrostatic force that a charge would experience at each point.
The charge that produces the field is called the source charge. A second charge placed in the field to investigate it is called the test charge.
Source charge and test charge
| Charge | Role |
|---|---|
| Source charge Q | Produces the electric field in the surrounding region |
| Test charge q | Experiences force and is used to determine the field at a point |
By convention, the test charge is positive. Its direction of force therefore defines the direction of E⃗. It must be extremely small so that its presence does not significantly redistribute charge or alter the original source field.
Definition of electric field intensity
Electric field intensity at a point is the electrostatic force experienced per unit positive test charge placed at that point.
- \vec E
- electric field intensity at the point (N·C⁻¹)
- \vec F
- electrostatic force on the test charge (N)
- q
- positive test-charge magnitude (C)
When to use: Use when the force on a known positive test charge is given.
When to use: Use to find the force on a charge placed in a known field.
For a negative charge placed in the field, q is negative in F⃗=qE⃗, so its force points opposite to the field direction.
Field due to a point source charge
For a source charge Q and a small positive test charge q separated by distance r, Coulomb's law gives the force:
- \hat r
- radial unit vector directed away from the source (none)
Dividing by q gives the electric field of the source charge. The test-charge magnitude cancels.
- Q
- source charge (C)
- r
- distance from the source charge (m)
- k
- Coulomb constant (N·m²·C⁻²)
When to use: Use this form for field magnitude; determine direction separately from the sign of Q.
Direction of electric field
| Source charge | Direction of E⃗ |
|---|---|
| Q>0 | Radially outward, because a positive test charge is repelled |
| Q<0 | Radially inward, because a positive test charge is attracted |
More generally, electric field direction is described from positive charge toward negative charge. At every point, it is the direction in which a unit positive test charge would move or tend to move.
Units and dependence
| Change | Effect on field magnitude |
|---|---|
| Q→2Q at fixed r | E→2E |
| r→2r at fixed Q | E→E/4 |
| r→3r at fixed Q | E→E/9 |
| r becomes very large | E approaches zero and becomes practically negligible |
The field of a point charge extends through space, although its strength decreases rapidly with distance according to the inverse-square law.
Textbook Example 10.2
Determine the electric field at the surface of a sphere of radius 3.0 m when a point charge of 9 μC is placed at its centre.
Because the central charge is positive, the field at the surface is directed radially outward.
Assignment 10.2 as guided practice
A conducting sphere carries a charge of 200 μC. Find the electric field intensity at a distance of 60 cm from its centre.
Exam-ready method
- Identify the source charge Q and observation distance r.
- Convert charge to coulombs and distance to metres.
- Use E=k|Q|/r² for the magnitude.
- State outward direction for Q>0 or inward direction for Q<0.
- If force and test charge are given, use E⃗=F⃗/q.
- Write the final unit as N·C⁻¹ or V·m⁻¹.
Exam Focus
Exam Focus
Important points
- Definitions of electric field and field intensity.
- Small positive test-charge convention.
- E⃗=F⃗/q and E⃗=kQ r̂/r².
- Units N·C⁻¹ and V·m⁻¹.
- Outward/inward direction and Example 10.2.
Important formulas
- E= Fq
- E=kQr2 r
- F=q E
Common exam traps
- The point-charge field formula contains source charge Q, not test charge q.
- Distance is measured from the centre and squared.
Long question structure
Field definition → source/test charges → E⃗=F⃗/q → Coulomb substitution → point-charge formula → direction → units → dependence and example
Common Mistakes
Common Mistakes
- Mistake
Including the test charge q in the final field formula E=k|Q|/r².
- Mistake
Defining field direction using a negative test charge instead of a positive one.
- Mistake
Writing inward field for a positive source or outward field for a negative source.
- Mistake
Forgetting to square the distance from the source charge.
- Mistake
Using centimetres or microcoulombs without converting to SI units.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
An electric field is the region around a source charge in which another charge experiences electrostatic force.
A test charge is chosen positive and sufficiently small so that it does not disturb the source field.
Electric field intensity is force per unit positive test charge: E⃗=F⃗/q.
For a point charge, E⃗=kQ r̂/r².
Electric field intensity at a point is the electrostatic force per unit positive test charge placed there.
E= Fq, E=kQr2 r
- Definition
- Electric field intensity at a point is the electrostatic force per unit positive test charge placed there.
- Formula
- E= Fq, E=kQr2 r
- Example
- For Q=9 μC at r=3.0 m, E=9×10³ N·C⁻¹ outward.
- Critical warning
- The source charge creates the field; the small positive test charge only measures it.
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Exam Practice
Important Question
Q1. Define electric field and electric field intensity.
Derivation
Q2. Derive the expression for electric field intensity due to a point charge.
Concept
Q3. Why is a small positive test charge used to define electric field direction?
Numerical
Q4. Solve textbook Example 10.2.
Reasoning
Q5. How does electric field intensity depend on source charge and distance?