Lessons › 5 Electricity and Magnetism › 5.3 ElectromagnetismPrevious lessonNext lesson

5.3.1 Moving Charges in Electric Fields

By the end of this lesson you can:

  • Describe the path of a charge in a uniform electric field
  • Calculate its acceleration and final speed
  • Compare the motion with projectile motion
Find your course: NSW Year 11: ElectrostaticsNSW Year 12: Module 6, IQ1QLDVIC Unit 3: Fields and motionAP Physics 2: Unit 10IB: D.3 Motion in electromagnetic fields
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🎥Watch
Learn the idea: a short explanation, then a check.

In the early 19th century, electricity and magnetism were viewed as two separate areas of physics. Through the experimental work of Michael Faraday and the subsequent mathematical synthesis by James Clerk Maxwell, these two fields were unified into the single framework of electromagnetism.

A central discovery of electromagnetism is that moving charges generate their own magnetic fields, causing them to experience a force when traveling through an external magnetic field. This fundamental interaction forms the operating principle behind electric motors.

Conversely, when electric charges experience a changing magnetic field—or a change in magnetic flux—a force is induced, generating an electromotive force (EMF). This principle forms the foundation of electrical power generation.

The following lessons examine the key physical principles and mathematical models that govern these electromagnetic behaviors.

Hand Rules Explained

Before we continue it's an important to learn the hand rules that are used in studying electromagnetism.
Hand rules are 'tool's used to establish the correct relationship between the vectors  of electrical current, force, EMF and magnetic field.
There are two in predominant use the first is Fleming's hand rules the second is the Palm rule. This video discusses both.
Both are equally valid, however it is best to consistently use one or the other.

Moving Charge behaviour in an Electric field

We know that stationary electric charges experience electrostatic forces when placed within an electric field. But what happens when a charged particle is already in motion as it enters a uniform electric field?

When a moving charge enters a uniform electric field perpendicularly, it experiences a constant force directed parallel to the field lines (F = qE). Because this force acts perpendicular to the particle's initial velocity, it produces a constant acceleration in one dimension while the perpendicular velocity remains unchanged. As a result, the charge follows a parabolic trajectory—much like a projectile moving through a gravitational field.

The following video uses the historic example of a Crookes tube (cathode ray tube) to demonstrate how magnetic and electric fields deflect beams of electrons, breaking down the underlying mathematical principles that govern moving charges in electric fields.

📝Practise
Worked examples first, then problems to try, then worksheets.

We are now ready to try a sample problem
Below is a sample problem with a video that explain how to solve it. It is suggested you try the problem beforehand, as this actually aids understanding, even if you are unsure if you are correct.

Picture
More problems to try

Practice Problems: Charges in a Uniform Electric Field

Electric field intensity can be written in N C−1 or V/m. Charge of an electron or proton: 1.60 × 10-19 C. Electron mass: 9.11 × 10-31 kg. Proton mass: 1.67 × 10-27 kg.

1. A positive test charge of 6.5 × 10-6 C experiences a force of 4.5 × 10-5 N. What is the magnitude of the electric field intensity?

Given: q = 6.5 × 10-6 C, F = 4.5 × 10-5 N

Formula: E = F / q

Calculation: E = (4.5 × 10-5) / (6.5 × 10-6) ≈ 6.92 N C−1

Answer: 6.9 N C−1
2. An electric field of intensity 150 V/m exists between two plates separated by 4.0 m. What is the potential difference between the plates?

Given: E = 150 V/m, d = 4.0 m

Formula: V = Ed

Calculation: V = 150 × 4.0 = 600 V

Answer: 600 V
3. A potential difference of 0.90 V exists from one side to the other of a cell membrane that is 5.0 × 10-9 m thick. What is the electric field across the membrane?

Given: V = 0.90 V, d = 5.0 × 10-9 m

Formula: E = V / d

Calculation: E = 0.90 / (5.0 × 10-9) = 1.8 × 108 V/m

Answer: 1.8 × 108 N C−1
4. An electron is released from rest at the negative plate of a pair of parallel plates in a vacuum. The potential difference between the plates is 250 V. (a) What is the change in the electron's kinetic energy as it crosses to the positive plate? (b) How fast is it moving when it arrives?

Given: V = 250 V, q = 1.60 × 10-19 C, m = 9.11 × 10-31 kg, vi = 0

(a) Change in kinetic energy: The work done by the field on the charge equals its change in kinetic energy, ΔEk = qV

ΔEk = 1.60 × 10-19 × 250 = 4.0 × 10-17 J

(b) Final speed: The electron starts from rest, so ΔEk = ½mv2

v = √(2 × 4.0 × 10-17 / 9.11 × 10-31) = √(8.78 × 1013) ≈ 9.4 × 106 m/s

Answer: (a) 4.0 × 10-17 J (250 eV), (b) 9.4 × 106 m/s
5. A proton is released from rest in a uniform electric field of 2.0 × 104 N C−1. It moves 0.030 m in the direction of the field. Find (a) the work done by the field on the proton, (b) the change in its kinetic energy and (c) its speed after moving this distance.

Given: E = 2.0 × 104 N C−1, d = 0.030 m, q = 1.60 × 10-19 C, m = 1.67 × 10-27 kg, vi = 0

(a) Work done: The force on the proton is F = qE = 1.60 × 10-19 × 2.0 × 104 = 3.2 × 10-15 N, in the direction of the field.

W = Fd = 3.2 × 10-15 × 0.030 = 9.6 × 10-17 J

(b) Change in kinetic energy: ΔEk = W = 9.6 × 10-17 J. (Check: V = Ed = 600 V, and qV = 9.6 × 10-17 J.)

(c) Final speed: v = √(2ΔEk / m) = √(2 × 9.6 × 10-17 / 1.67 × 10-27) ≈ 3.4 × 105 m/s

Answer: (a) 9.6 × 10-17 J, (b) 9.6 × 10-17 J, (c) 3.4 × 105 m/s
🕹️Explore
Test your predictions in a simulation.

​This is a simulation of a charged particle being shot into a uniform electric field. ​By Tom Walsh
One way to use this is to change one variable at a time and

  1. predict the charge behaviour
  2. Run the simulation
  3. Explain the results in terms of the concepts here, as well as other physics principles

Here is another interactive animation to play with