Force on a Moving Charge(OCR A Level Physics)

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Katie M

Expertise

Physics

Force on a Moving Charge

• The magnetic force on an isolated moving charged particle, such as a proton, is given by the equation:

F = BQv

• Where:
• F = magnetic force on the particle (N)
• B = magnetic flux density (T)
• Q = charge of the particle (C)
• v = speed of the particle (m s1)

• This is the maximum force on the charged particle, when F, B and v are mutually perpendicular
• Therefore if a particle travels parallel to a magnetic field, it will not experience a magnetic force

• Current is the rate of flow of positive charge
• This means that the direction of the 'current' for a flow of negative charge (e.g. an electron beam) is in the opposite direction to its motion

• If the charged particle is moving at an angle θ to the magnetic field lines, then the size of the magnetic force F is given by the equation:

F = BQv sin θ

• This equation shows that:
• The size of the magnetic force is zero if the angle θ is zero (i.e. the particle moves parallel to the field lines)
• The size of the magnetic force is maximum if the angle θ is 90° (i.e. the particle moves perpendicular to field lines)

Worked example

A beta particle is incident at 70° to a magnetic field of flux density 0.5 mT, travelling at a speed of 1.5 × 106 m s–1.

Calculate:

a) The magnitude of the magnetic force on the beta particle

b) The magnitude of the maximum possible force on a beta particle in this magnetic field, travelling with the same speed

Part (a)

Step 1: Write out the known quantities

• Magnetic flux density B = 0.5 mT = 0.5 × 103 T
• Speed v = 1.5 × 106 m s–1
• Angle θ between the flux and the velocity = 70°

Step 2: Substitute quantities into the equation for magnetic force on a charged particle

• A beta particle is an electron
• Therefore, the magnitude of electron charge Q = 1.6 × 10–19 C
• Substituting values gives:

BQv sin θ

F = (0.5 × 10–3) × (1.6 × 10–19) × (1.5 × 106) × sin (70)

F = 1.1 × 10–16 N

Part (b)

Step 1: Write out the known quantities

• Magnetic flux density B = 0.5 mT = 0.5 × 10–3 T
• Speed v = 1.5 × 106 m s–1

Step 2: Determine the angle to the flux lines

• Angle θ between the flux and the velocity = 90° if the magnetic force is a maximum

Step 3: Substitute quantities into the equation for magnetic force on a charged particle

• The magnitude of electron charge Q = 1.6 × 10–19 C
• Substituting values gives:

BQv sin θ BQv when sin 90 = 1

F = (0.5 × 10–3) × (1.6 × 10–19) × (1.5 × 106)

F = 1.2 × 10–16 N

Exam Tip

Remember not to mix this up with F = BIL sin θ!

• F = BIL sin θ is the force on a current-carrying conductor
• F = BQv sin θ is the force on an isolated moving charged particle (which may be inside a conductor)

Another super important fact to remember for typical exam questions is that the magnetic force on a charged particle is centripetal, because it always acts at 90° to the particle's velocity. You should practise using Fleming's Left Hand Rule to determine the exact direction!

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Author:Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.