Electric Fields
Investigate the forces between charged particles, map electric field patterns, and understand how potential difference drives charge flow in circuits and beyond.
Coulomb's Law
Coulomb's law describes the electrostatic force between two point charges. Like gravity, it follows an inverse-square relationship. Unlike gravity, the electric force can be attractive or repulsive depending on the signs of the charges.
The Coulomb Force Equation
F = kq1q2 / r2
k (Coulomb constant)
8.99 × 109 N m2 C-2
q1, q2
Charges in coulombs (C)
r
Distance between charge centres (m)
Like charges REPEL
Positive force (repulsion)
Unlike charges ATTRACT
Negative force (attraction)
Electric Field Lines and Field Strength
An electric field exists around any charged object. The electric field strength E at a point is the force per unit positive charge placed at that point: E = F/q. Field lines show the direction a positive test charge would move.
Electric Field Patterns
Positive point charge
Lines radiate outward
Negative point charge
Lines point inward
Parallel plates
Uniform field between plates
Key Equations
Point charge field: E = kq/r2 (N C-1)
Uniform field (parallel plates): E = V/d where V is the potential difference and d is the plate separation
Force on a charge in a field: F = qE
Electric Potential and Potential Difference
Electric potential (V) at a point is the work done per unit charge in bringing a positive test charge from infinity to that point. The potential difference between two points is what drives charge flow and determines the energy gained or lost by charges moving between those points.
Energy and Potential
Electric potential (point charge)
V = kq/r (volts, V)
Work done on a charge
W = qΔV (joules, J)
Kinetic energy gained
½mv2 = qΔV
The Electronvolt (eV)
In particle physics, energy is often measured in electronvolts. One electronvolt is the energy gained by one electron accelerated through a potential difference of 1 V:
1 eV = 1.60 × 10-19 J
Key Vocabulary
Electric Field Strength (E)
The force per unit positive charge at a point in an electric field. Measured in N C-1 or equivalently V m-1.
Coulomb's Law
The electrostatic force between two point charges: F = kq1q2/r2. Attractive for unlike charges, repulsive for like charges.
Potential Difference
The work done per unit charge in moving a charge between two points in an electric field. Measured in volts (V = J C-1).
Uniform Electric Field
A field with constant strength and direction at every point, produced between two parallel charged plates. Field lines are equally spaced and parallel.
Worked Examples
Calculate the force between two charges of +3.0 μC and -5.0 μC separated by 0.20 m.
Step 1: Convert: q1 = 3.0 × 10-6 C, q2 = 5.0 × 10-6 C
Step 2: F = kq1q2/r2 = (8.99 × 109)(3.0 × 10-6)(5.0 × 10-6) / (0.20)2
Step 3: F = 1.349 × 10-1 / 0.04 = 3.4 N (attractive)
Answer: The force is 3.4 N of attraction, since the charges have opposite signs.
Two parallel plates are separated by 5.0 mm with a potential difference of 200 V. Find the electric field strength between them.
Step 1: E = V/d = 200 / (5.0 × 10-3)
Answer: E = 40,000 V m-1 = 4.0 × 104 N C-1
An electron is accelerated from rest through a potential difference of 500 V. Find its final speed. (me = 9.11 × 10-31 kg, e = 1.60 × 10-19 C)
Step 1: Energy gained: W = qΔV = (1.60 × 10-19)(500) = 8.0 × 10-17 J
Step 2: ½mv2 = 8.0 × 10-17
Step 3: v = √(2 × 8.0 × 10-17 / 9.11 × 10-31) = √(1.756 × 1014)
Answer: v ≈ 1.33 × 107 m s-1 (about 4.4% the speed of light)
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Two positive charges are brought closer together. The electrostatic force between them:
Question 2
Electric field lines around a single positive point charge:
Question 3
In a uniform electric field between parallel plates, the field strength is:
Question 4
An electron accelerated through 1000 V gains kinetic energy of:
Question 5
Comparing Coulomb's law and Newton's law of gravitation, one key difference is:
Key Concepts Summary
- ●Coulomb's law: F = kq1q2/r2 describes the force between point charges -- attractive for unlike charges, repulsive for like charges.
- ●Electric field strength: E = F/q = kq/r2 for point charges; E = V/d for uniform fields between parallel plates.
- ●Field lines point away from positive charges and toward negative charges. They show the direction of force on a positive test charge.
- ●Potential difference (V) drives charge flow. Work done: W = qΔV. Charges gain kinetic energy when accelerated through a potential difference.
- ●The electronvolt (1 eV = 1.60 × 10-19 J) is a convenient energy unit for atomic and subatomic processes.