Edexcel A Level (IAL) Physics-4.26 Magnetic Force on a Charged Particle- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -4.26 Magnetic Force on a Charged Particle- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -4.26 Magnetic Force on a Charged Particle- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
Force on a Charged Particle in a Magnetic Field
When a charged particle moves through a magnetic field, it experiences a force provided the motion is not parallel to the field. This force is always perpendicular to both the direction of motion and the magnetic field.
Magnetic Force on a Moving Charge
The magnitude of the magnetic force on a charged particle is given by:
\( F = Bqv\sin\theta \)
- \( F \) = magnetic force (N)
- \( B \) = magnetic flux density (T)
- \( q \) = charge on the particle (C)
- \( v \) = speed of the particle (m s⁻¹)
- \( \theta \) = angle between the velocity and the magnetic field
Key Features of the Magnetic Force
- The force acts only when the charge is moving.
- The force is maximum when \( \theta = 90^\circ \).
- The force is zero when the particle moves parallel to the field.
- The force changes the direction of motion but not the speed.
Maximum force: \( F = Bqv \)
Zero force: \( \theta = 0^\circ \)
Direction of the Force — Fleming’s Left-Hand Rule
Fleming’s left-hand rule is used to determine the direction of the force on a positive charge.
- First finger → direction of magnetic field (N to S)
- Thumb → direction of force (motion of positive charge)
- Second finger → direction of current (or velocity of positive charge)
Important note:
- For a negative charge (e.g. electron), the force is in the opposite direction to that given by the rule.
Motion of Charged Particles in a Magnetic Field
Particle enters perpendicular to the field:
- Force is always perpendicular to velocity.
- Particle moves in a circular path.
- Magnetic force provides the centripetal force.
Particle enters at an angle:
- Velocity has components parallel and perpendicular to the field.
- Motion becomes helical (spiral).
Relation to Circular Motion
For motion perpendicular to the field:
\( Bqv = \dfrac{mv^2}{r} \)
This shows the magnetic force provides the centripetal force.
Example (Easy)
A proton moves at right angles to a magnetic field of flux density \( 0.30\ \mathrm{T} \) with speed \( 2.0\times10^6\ \mathrm{m\,s^{-1}} \). Calculate the magnetic force on the proton. (Charge of proton \( = 1.6\times10^{-19}\ \mathrm{C} \))
▶️ Answer / Explanation
Since motion is perpendicular, \( \sin\theta = 1 \).
\( F = Bqv = 0.30 \times 1.6\times10^{-19} \times 2.0\times10^6 \)
\( F = 9.6\times10^{-14}\ \mathrm{N} \)
Example (Medium)
An electron enters a magnetic field at an angle of \( 30^\circ \) to the field direction. Explain whether it experiences a magnetic force.
▶️ Answer / Explanation
- The electron has a velocity component perpendicular to the field.
- Since \( \sin 30^\circ \neq 0 \), a magnetic force acts.
- The force direction is opposite to that for a positive charge.
Example (Hard)
A charged particle moves parallel to a uniform magnetic field. Explain its subsequent motion.
▶️ Answer / Explanation
- Angle between velocity and field is \( 0^\circ \).
- \( \sin 0^\circ = 0 \), so magnetic force is zero.
- The particle continues in a straight line at constant speed.