# 25.3.2 Force on a Moving Charge

### Calculating Magnetic Force on a Moving Charge

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

F = BQv sinθ

• Where:
• F = force on the charge (N)
• B = magnetic flux density (T)
• v = speed of the charge (m s-1)
• θ = angle between charge’s velocity and magnetic field (degrees)
• Equivalent to the force on a wire, if the magnetic field B is perpendicular to the direction of the charge’s velocity, the equation simplifies to:

F = BQv

• According to Fleming’s left hand rule:
• When an electron enters a magnetic field from the left, 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) is now the direction of velocity v of the positive charge

#### Worked example: Calculating magnetic force on a moving electron

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

Angle between electron and magnetic field, θ = 30o

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

F = BQv sinθ

Step 3:            Substitute in values, and calculate the force on the electron at 30o

F = (0.2) × (1.60 × 10-19) × (5.3 × 107) × sin(30) = 8.5 × 10-13 N

Step 4:            Calculate the electron force when travelling perpendicular to the field

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

Step 5:            Calculate the ratio of the perpendicular force to the force at 30o

Therefore, the force on the electron is twice as strong when it is moving perpendicular to the field than when it is moving at 30o to the field

#### 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: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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