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D.3.1—Charge in electric fields

Syllabus
First assessment 2025
Objective
—
Level
HL

Model Charge Motion in an Electric Field

Start with the force

A charge in a uniform electric field experiences F=qEF=qE. A positive charge accelerates in the field direction; a negative charge accelerates opposite to it. In vacuum, if the field is uniform, the acceleration is constant: a=qE/ma=qE/m.

Read the trajectory

A particle initially moving perpendicular to a uniform electric field has constant velocity in the direction perpendicular to the field and constant acceleration along the field, so its path is parabolic. A particle initially at rest accelerates along a field line.

Solve the motion

Find the force and acceleration direction first, then use constant-acceleration equations. The time in the field comes from motion along the entry direction; the transverse displacement comes from the electric acceleration.

Common trap

Do not make an electron accelerate in the electric-field direction. The field direction is defined for a positive charge; an electron accelerates toward the positive plate.

D.3.1 Exam Analysis

Assessment in practice

1 marks
How it is assessed

Questions state the acceleration direction of an electron or analyse a charged particle’s parabolic path through a field.

Command terms

State

What earns marks

Use F=qE and a=qE/m, reverse the acceleration direction for a negative charge, and separate longitudinal constant velocity from transverse constant acceleration.

Watch for

Using the field direction as the acceleration direction for an electron, or treating transverse electric-field motion as constant speed.

Representative question

Question 1

[Maximum number: 1]

An electron of mass mem_{\mathrm{e}} and charge e accelerates between two plates separated by a distance s in a vacuum. The potential difference between the plates is V.

What is the acceleration of the electron?

A

meeVs\frac{m_{\mathrm{e}} e V}{s}

B

meVes\frac{m_{\mathrm{e}} V}{e s}

C

eVmes\frac{e V}{m_{\mathrm{e}} s}

D

Vmees\frac{V}{m_{\mathrm{e}} e s}

Retrieve the D.3 Motion in Electromagnetic Fields Model

D.3 is secure when you can keep electric and magnetic force rules separate and then combine them deliberately.

  • Electric fields give F=qE and constant acceleration in a uniform field
  • Magnetic fields bend moving charges without changing kinetic energy
  • Crossed fields can cancel at v=E/B
  • Moving-charge magnetic force is F=|q|vB sinθ
  • Conductor force is F=BIL sinθ
  • Parallel currents attract in the same direction and repel in opposite directions