# Motion of Charged Particles in a B Field(OCR A Level Physics)

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Ashika

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## Motion of a Charged Particle in a Magnetic Field

• A charged particle in uniform magnetic field which is perpendicular to its direction of motion travels in a circular path
• This is because the magnetic force F will always be perpendicular to its velocity v
• F will always be directed towards the centre of the path in circular motion

A charged particle moves travels in a circular path in a magnetic field

• The magnetic force F provides the centripetal force on the particle
• The equation for centripetal force is:

• Where:
• F = centripetal force (N)
• m = mass of the particle (kg)
• v = linear velocity of the particle (m s1)
• r = radius of the orbit (m)

• Equating this to the magnetic force on a moving charged particle gives the equation:

• Rearranging for the radius r obtains the equation for the radius of the orbit of a charged particle in a perpendicular magnetic field:

• This equation shows that:
• Faster moving particles with speed v move in larger circles (larger r): r v
• Particles with greater mass m move in larger circles: r m
• Particles with greater charge q move in smaller circles: r ∝ 1 / q
• Particles moving in a strong magnetic field B move in smaller circles: r ∝ 1 / B

• The centripetal acceleration is in the same direction as the centripetal (and magnetic) force
• This can be found using Newton's second law:

F = ma

#### Worked example

An electron with a charge-to-mass ratio of 1.8 × 1011 C kg1 is travelling at right angles to a uniform magnetic field of flux density 6.2 mT. The speed of the electron is 3.0 × 106 m s1.

Calculate the radius of the circular path of the electron.

#### Exam Tip

Make sure you're comfortable with deriving the equation for the radius of the path of a particle travelling in a magnetic field, as this is a common exam question.

Similar to orbits in a gravitational field, any object moving in circular motion will obey the equations of circular motion. Make sure to refresh your knowledge of these equations.

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