20.3 Force on a Moving Charge

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Determine the direction of the force on a charge moving in a magnetic field
  2. Recall and use F = BQv sin θ
  3. Understand the origin of the Hall voltage and derive and use V_H = BI / (ntq)
  4. Understand the use of a Hall probe to measure magnetic flux density
  5. Describe the motion of a charged particle moving in a uniform magnetic field perpendicular to its direction of motion
  6. Explain how electric and magnetic fields can be used in velocity selection

1. Direction of the Force on a Moving Charge

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Why does a moving charge experience a force?

A moving charge creates its own small magnetic field around it. When this moving charge enters an external magnetic field, the two fields interact and produce a force on the charge. This force is always perpendicular (at right angles) to both the velocity of the charge and the direction of the magnetic field.

Key point: A charge that is stationary (not moving) feels no magnetic force. The force only exists when the charge is moving.

Using Fleming's Left-Hand Rule (LHR)

To find the direction of the magnetic force on a moving charge, you use Fleming's Left-Hand Rule. Hold your left hand with your thumb, first finger, and second finger all pointing at right angles to each other:

  • Thumb → direction of the Force (motion of the charge)
  • First finger → direction of the magnetic Field (B)
  • Second finger → direction of the conventional Current (flow of positive charge)

Conventional current means the direction positive charges would flow — from positive to negative. This is the agreed direction physicists use, even though in metals it is actually electrons (negative charges) that move.

Positive vs Negative Charges

This is where students often make mistakes, so read carefully:

  • For a positive charge: the current direction is the same as the direction of motion of the charge. Point your second finger in the same direction the charge is moving.
  • For a negative charge (like an electron): the current direction is opposite to the direction of motion. Point your second finger in the opposite direction to the electron's movement.

Example: An electron moves to the right in a magnetic field directed into the page.

  • The current direction for an electron is to the left (opposite to its motion)
  • First finger (field): into the page
  • Second finger (current): to the left
  • Thumb (force): upward → the electron is pushed upward

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