The Effect of Magnetic and Electric Fields on Alpha and Beta Particles
CSEC Physics: Charged Particles in Fields
Essential Understanding: Alpha and beta particles are charged, so they are affected by magnetic and electric fields. The direction and amount of deflection depends on the charge and mass of each particle. This is key evidence for the nature of these particles!
The Lorentz Force
When a charged particle moves through a magnetic field, it experiences a force called the Lorentz force. This force is perpendicular to both the particle's velocity and the magnetic field direction.
The Lorentz Force Formula
Where:
F = Force (N) | B = Magnetic field strength (T) | q = Charge (C)
v = Velocity (m/s) | θ = Angle between velocity and field
Key Relationships
Charge Effect: Force is proportional to charge. Alpha (+2) experiences twice the force of beta (-1) at same speed.
Mass Effect: Lighter particles curve more. Radius r = mv/qB. Beta particles curve much more than alpha.
Direction: Positive charges deflect one way, negative charges deflect opposite way in same field.
Magnetic Field Effects
Alpha (+2): Curves in one direction. Large radius (heavy, high momentum).
Beta (-1): Curves in opposite direction. Small radius (light, low momentum).
Gamma (0): No deflection (uncharged).
Fleming's Left Hand Rule
Fleming's Left Hand Rule helps determine the direction of force on a positive charge:
Field direction (N to S)
Current (positive charge flow)
Force (motion)
Important Note on Beta Particles
Since beta particles are negatively charged, Fleming's Left Hand Rule gives the direction for positive charge flow. For negative charges, remember to reverse the direction!
Alternatively, use the Right Hand Rule for negative charges or simply remember: Alpha curves one way, Beta curves the opposite way in the same field.
Electric Field Effects
In an electric field, charged particles experience a force toward or away from the plates depending on their charge.
Electric Force
Alpha (+2): Attracted toward negative plate, follows curved path
Beta (-1): Attracted toward positive plate, follows curved path
Gamma (0): No deflection (uncharged)
Interactive Field Simulation
Observe Deflection in Magnetic Field
Objective: Fire alpha and beta particles into a magnetic field and observe how they deflect in opposite directions due to their opposite charges.
Click a button to fire particles into the magnetic field
The magnetic field (represented by X symbols) goes into the page. Observe the deflection directions!
Comparison of Deflection
| Property | Alpha (α) | Beta (β) | Gamma (γ) |
|---|---|---|---|
| Charge | +2e | -e | 0 |
| Mass | 4 u (heavy) | 1/1836 u (light) | 0 |
| Magnetic Deflection | Curves one way | Curves opposite way | No deflection |
| Electric Deflection | Toward negative plate | Toward positive plate | No deflection |
| Radius of Curvature | Large (high momentum) | Small (low momentum) | Infinite (no curve) |
| Force Magnitude | 2× stronger (|q| = 2) | Weaker (|q| = 1) | Zero |
Radius of Curvature
The radius of the circular path depends on the particle's momentum and charge:
$$ r = \frac{mv}{Bq} $$
This shows that lighter particles (smaller m) have smaller radii, and more highly charged particles (larger q) have smaller radii.
Remember the Pattern
Same Field, Opposite Directions: Alpha and beta particles always deflect in opposite directions in both magnetic and electric fields because they have opposite charges.
Same Field, Different Radii: Beta particles curve much more sharply than alpha particles because they are much lighter.
Gamma Never Deflects: Since gamma rays have no charge, they pass through both magnetic and electric fields in straight lines.
CSEC Practice Arena
Test Your Understanding
1. Direction of Deflection: Alpha particles (+2 charge) will curve in one direction, while beta particles (-1 charge) will curve in the opposite direction because they have opposite charges.
2. Radius of Curvature: Alpha particles will follow a wider curve (larger radius) because they are much heavier (7300× more mass) and have higher momentum. Beta particles will follow a sharper curve (smaller radius) because they are very light.
3. Summary: Alpha curves gently one way; Beta curves sharply the opposite way.
Setup: Top plate positive (+), Bottom plate negative (-)
Force on Alpha: Alpha particles have a positive charge (+2) and are attracted to the negative plate (bottom).
Path: Alpha particles will curve downward toward the negative plate, following a parabolic path similar to projectile motion under gravity.
Key Point: Positive charges are always attracted toward the negative plate and repelled by the positive plate.
Magnetic Fields: The Lorentz force F = Bqv sinθ depends on charge q. If q = 0, then F = 0, so there is no force to deflect the particle.
Electric Fields: The electric force F = Eq also depends on charge q. If q = 0, then F = 0.
Result: Uncharged particles (like gamma rays and neutrons) are not affected by electromagnetic fields and travel in straight lines.
1. Particle A (gentle left curve): Alpha particle (α) - Curves gently due to large mass, and curves left (let's say that's the positive deflection direction).
2. Particle B (sharp right curve): Beta particle (β) - Curves sharply due to small mass, and curves right (opposite to alpha because negative charge).
3. Particle C (straight line): Gamma ray (γ) - No deflection because gamma rays have no electric charge.
Chapter Summary
Magnetic Field Effects
- Alpha: Curves one way, large radius
- Beta: Curves opposite way, small radius
- Gamma: No deflection
Electric Field Effects
- Alpha: Toward negative plate
- Beta: Toward positive plate
- Gamma: No deflection
Remember!
Alpha (+2) and Beta (-1) always deflect in opposite directions!