# CIE A Level Physics复习笔记20.1.5 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)
• Q = charge of the particle (C)
• v = speed of the charge (m s-1)
• θ = angle between charge’s velocity and magnetic field (degrees) The force on an isolated moving charge is perpendicular to its motion and the magnetic field B

• 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, 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) is now the direction of velocity v of the 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 at 30° to the field, and state the factor it increases by compared to when it travels 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

Angle between electron and magnetic field, θ = 30°

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 30°

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