The Force on a Charged Particle in a Magnetic Field
The force on a charged particle moving in a magnetic field is given by the following equation:
* F = qvB sin θ
Where:
* F is the force on the particle
* q is the charge of the particle
* v is the velocity of the particle
* B is the magnetic field strength
* θ is the angle between the velocity and the magnetic field
The Relationship Between Mass and Deflection
The force on the particle causes it to accelerate and change direction. The amount of deflection is related to the particle's acceleration, which is determined by Newton's Second Law:
* F = ma
Where:
* m is the mass of the particle
* a is the acceleration of the particle
Putting it Together
If we combine these two equations, we get:
* ma = qvB sin θ
Solving for acceleration:
* a = (qvB sin θ) / m
This equation shows that the acceleration (and therefore the deflection) is inversely proportional to the mass of the particle.
Conclusion
A more massive particle will experience less acceleration for the same force, resulting in a smaller angle of deflection in a magnetic field.
