A LevelPhysicsCIERevision Notes20. Magnetic Fields20.3 Force on a Moving ChargeForce on a Moving Charge

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First teaching 2023

First exams 2025

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Force on a Moving Charge (CIE A Level Physics)

Revision Note

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Calculating Magnetic Force on a Moving Charge

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

F space equals space B Q v sin open parentheses theta close parentheses

  • 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)

Path of a moving charged particle in a magnetic field

Force on isolated moving charge, downloadable AS & A Level Physics revision notes

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 space equals space B Q v

  • 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 downwards
  • 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

Direction of Magnetic Force, downloadable AS & A Level Physics revision notes

The direction of the magnetic force F on positive and negative particles in a B field in and out of the page

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.

Answer:

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 space equals space B Q v sin open parentheses theta close parentheses

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

F space equals space open parentheses 0.2 close parentheses space cross times space open parentheses 1.60 space cross times space 10 to the power of negative 19 end exponent close parentheses space cross times space open parentheses 5.3 space cross times space 10 to the power of 7 close parentheses space cross times space sin open parentheses 30 close parentheses space equals space 8.5 space cross times space 10 to the power of negative 13 end exponent space straight N

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

F space equals space open parentheses 0.2 close parentheses space cross times space open parentheses 1.60 space cross times space 10 to the power of negative 19 end exponent close parentheses space cross times space open parentheses 5.3 space cross times space 10 to the power of 7 close parentheses space equals space 1.696 space cross times space 10 to the power of negative 12 end exponent space straight N

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

fraction numerator 1.696 space cross times 10 to the power of negative 12 end exponent over denominator 8.5 space cross times space 10 to the power of negative 13 end exponent end fraction space equals space 1.992 space equals space 2

  • 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)

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    Ashika

    Author: Ashika

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