CCEA A-Level Physics 1210
Physical Quantities, Scalars and Vectors
Moments and Equilibrium
Linear Motion and Dynamics
Newton's Laws of Motion
Linear Momentum and Impulse
Work, Energy and Power
Current, Charge and Potential Difference
Resistance and Resistivity
Internal Resistance and Potential Dividers
Waves
Refraction
Lenses
Superposition, Interference and Diffraction
Quantum Physics
Wave-Particle Duality
Astronomy
Practical Skills and Data Analysis
Deformation of Solids
Thermal Physics
Uniform Circular Motion
Simple Harmonic Motion
The Nucleus and Radioactive Decay
Nuclear Energy, Fission and Fusion
Gravitational Fields
Electric Fields
Capacitors
Magnetic Fields
Charged Particles and Accelerators
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.
What provides the centripetal force when a charged particle moves in a circle in a magnetic field?
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
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
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
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
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
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
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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