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Charged Particles and Accelerators

Circular paths in a magnetic field

  • 3 things to know
  • Unit A2 2

Overview

Recall questions on the magnetic force as the centripetal force, the derivation of r = mv/(Bq) with every symbol, the effect of doubling the speed or the flux density, worked radius calculations for an electron, why the charge to mass ratio decides the radius, the period T = 2πm/(Bq) and why it does not depend on speed.

What you need to know

Answer each one before you reveal it.

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Key term

Define each symbol in r = mv/(Bq).

Key term

What provides the centripetal force when a charged particle moves in a circle in a magnetic field?

Key term

How does the radius of a charged particle's circular path in a magnetic field change if its speed is doubled?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What provides the centripetal force when a charged particle moves in a circle in a magnetic field?

    Model answer

    The magnetic force Bqv, which always points towards the centre of the circular path.

  2. 2

    Derive the equation for the radius of the circular path.

    Model answer

    Setting Bqv equal to mv²/r and cancelling one factor of v gives r = mv/(Bq).

  3. 3

    Define each symbol in r = mv/(Bq).

    Model answer

    r is the radius in metres, m the mass in kilograms, v the speed in m s⁻¹, B the flux density in tesla and q the charge in coulombs.

  4. 4

    How does the radius change if the particle's speed is doubled?

    Model answer

    The radius doubles, since radius is proportional to speed at fixed field and charge to mass ratio.

  5. 5

    How does the radius change if the flux density is doubled?

    Model answer

    The radius halves, since radius is inversely proportional to the flux density.

  6. 6

    Calculate the radius of the path of an electron travelling at 2.0 × 10⁷ m s⁻¹ in a field of 0.050 T.

    Model answer

    r = mv/(Bq) = 9.11 × 10⁻³¹ × 2.0 × 10⁷ ÷ (0.050 × 1.60 × 10⁻¹⁹) = 1.82 × 10⁻²³ ÷ 8.0 × 10⁻²¹, which is 2.3 × 10⁻³ m.

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