# 7.8.4 Force on a Moving Charge

### Calculating Magnetic Force on a Moving Charge

• The magnetic force on an isolating moving charged particle, such as an electron, is given by the equation:

F = BQv

• Where:
• F = magnetic force on the particle (N)
• B = magnetic flux density (T)
• Q = charge of the particle (C)
• v = speed of the particle (m s-1)

• Current is the rate of flow of positive charge
• This means that the direction of the current for a flow of negative charge (eg. an electron beam) is in the opposite direction to its motion
• F, B and v are mutually perpendicular
• Therefore if a particle travels parallel to a magnetic field, it will not experience a magnetic force

The force on an isolated moving charge is perpendicular to its motion and the magnetic field B

• According to Fleming’s left hand rule:
• B is directed into the page, and current I (or speed v) is directed to the right
• When an electron enters a magnetic field from the left, and if the magnetic field is directed into the page, then the force on it will be directed upwards
• The equation shows:
• If the direction of the electron changes, the magnitude of the force will change too
• The force due to the magnetic field is always perpendicular to the velocity of the electron
• Note: this is equivalent to circular motion
• Fleming’s left-hand rule can be used again to find the direction of the force, magnetic field and velocity
• The key difference is that the second finger, representing current I (direction of positive charge), can now be used as the direction of velocity v of a positive charge

#### Worked Example

An electron is moving at 5.3 × 107 m s-1 in a uniform magnetic field of flux density 0.2 T.

Calculate the force on the electron when it is moving perpendicular to the field.

Step 1: Write out the known quantities

• Speed of the electron, v = 5.3 × 107 m s-1
• Charge of an electron, Q = 1.60 × 10-19 C
• Magnetic flux density, B = 0.2 T

Step 2: Write down the equation for the magnetic force on an isolated particle

F = BQv

Step 3: Substitute in values, and calculate the force on the electron

F = (0.2) × (1.60 × 10-19) × (5.3 × 107) = 1.696 × 10-12 N

#### Exam Tip

Remember not to mix this up with F = BIL!

• F = BIL is for a current-carrying conductor
• F = BQv is for an isolated moving charge (which may be inside a conductor)

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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