20.3.2Magnetic fields and alternating currents (A Level)
Force on a Moving Charge
5 min read 9 parts Lesson 7 of 24 1 quiz
Lesson summary
20.3.2 Force on a Moving Charge — AS PHYSICS 9702 notes: Use F = Bqv sin θ for the magnetic force on a moving charged particle.Current in a wire — made of many moving carriers, with I = nAvqn is the number density of carriersA is the cross-sectional areav is the drift speedq is t…
- Force on the wire
- Per carrier
- Perpendicular
- Speed and energy
- Stationary charge
- Both fields present
Section 1 of 9From a current to a single charge
Current in a wire
- Current in a wire made of many moving carriers, with I = nAvq
- n is the number density of carriers
- A is the cross-sectional area
- v is the drift speed
- q is the charge on each carrier
Force on the wire
- Ftotal = B(nAvq)L sin θ = (nAL) × (Bqv sin θ)
Per carrier
- Per carrier dividing by the nAL carriers in length L gives F = Bqv sin θ
Section 2 of 9The equation
F
Bqv sin θ
- the force on a particle moving at an angle θ to the field
- F is in N
- B is in T
- q is in C, and |q| = e = 1.60 × 10⁻¹⁹ C for an electron or proton
- v is in m s⁻¹
- θ is the angle between velocity and field
Maximum
- F = Bqv when the velocity is perpendicular to the field
Zero
- Zero when the particle moves along the field, or is stationary
Direction
- Fleming's left-hand rule, with the second finger along conventional current
- For a negative charge the second finger points opposite to the velocity
Section 3 of 9Properties of the force
Perpendicular
- Perpendicular the force is always at right angles to the velocity
Speed and energy
- Speed and energy it changes the direction of travel but not the speed or kinetic energy
No work
- No work the force does no work on the particle
Path
- Path a curve, which is a circle when v is perpendicular to a uniform field
Stationary charge
- Stationary charge v = 0 means no magnetic force at all
Section 4 of 9Comparing electric and magnetic forces
| Property | Electric field | Magnetic field |
|---|---|---|
| Force on stationary charge | qE | zero |
| Direction | along the field line | perpendicular to field and velocity |
| Work done on charge | yes, changes kinetic energy | none |
| Path of charge entering at right angles | parabola | circle (arc) |
- Both fields present
- total force is qE + Bqv, leading to the velocity selector
Section 5 of 9Checking units
F = Bqv
- N A⁻¹ m⁻¹ × A s × m s⁻¹ = NWhat the symbols mean: F = force on the moving charge (N) · B = magnetic flux density (T) · q = charge (C) · v = speed (m s−1)
F = BIL
- N A⁻¹ m⁻¹ × A × m = NWhat the symbols mean: F = force on the wire (N) · B = magnetic flux density (T) · I = current (A) · L = length of wire in the field (m) · θ = angle between wire and field
Alternative tesla
- Alternative tesla the flux density in which 1 C moving at 1 m s⁻¹ at right angles to the field experiences a force of 1 N
- It is equivalent to the wire definition
Mass
- Mass at these speeds use the rest mass
Section 6 of 9Using the equation
Using the equation
Type 1
- Type 1 given B, q and v, find F
Type 2
- Type 2 given a force from an observed deflection, find B or v
Type 3
- Type 3 find the acceleration, a = F/m
Electrons and protons
- Electrons and protons electron mass is 9.11 × 10⁻³¹ kg and proton mass is 1.67 × 10⁻²⁷ kg,
- so the same force gives an electron about 1800 times the acceleration
Units
- Units convert speeds given as fractions of c or in km s⁻¹, and charges in μC or multiples of e
Section 7 of 9More from the specification
1Hall effect and Hall voltage
- When a current-carrying semiconductor slice is placed in a transverse magnetic field, Lorentz forces deflect mobile charge carriers to one side, inducing a transverse Hall voltage: VH = (B I) / (n q t).
2Hall probes for magnetic field measurement
- Hall effect probes produce an electrical potential difference directly proportional to magnetic flux density B, serving as calibrated digital Gaussmeters.
3Carrier density determination
- Measuring Hall voltage across materials with known current and dimensions allows physicists to calculate majority charge carrier density n and determine carrier polarity.
4Hall voltage derivation
- Hall voltage derivation magnetic deflection of charge carriers across conductor plates generates transverse Hall voltage VH = BI / (ntq).
5Circular motion trajectory
- Circular motion trajectory magnetic force acts perpendicularly to velocity, providing centripetal acceleration to bend charges along a circular arc.
6Hall probe field strength
- Hall probe field strength rotating a calibrated semiconductor Hall probe determines magnitude and direction of magnetic flux density.
7Field lines
- Lines showing the direction and strength of a magnetic field.
8Conductor
- Material that allows current to flow.
9Radius
- Distance from the centre to the circular path.
10Field strength
- G = Fg/m.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Magnetic force on a moving charge | F = Bqv sin θ |
| Drift speed | the average speed of charge carriers in a wire |
| Number density | n, the number of carriers per unit volume |
| Centripetal force | the force towards the centre of a circular path |
| Rest mass | the mass of a particle at rest |
| Flux density | B, in tesla |
Section 9 of 9Exam technique
1
Using F = BIL for an isolated charge — F = BQv is for a moving charge, F = BIL for a conductor.
2
Saying the force changes the speed — it changes only direction.
3
Forgetting sin θ — the angle is between velocity and field.
4
Giving a force for a stationary charge — it is zero.