Theme D — Fields
D.3.2 Magnetic Force between Two Parallel Conductors — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 29 of 39 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
D.3.2 Magnetic Force between Two Parallel Conductors — IB PHYSICS SL notes: Explain why two parallel current-carrying wires attract or repel and calculate the force per unit length.Field of a current — every current-carrying wire creates a magnetic field around itselfThe field di…
- Second wire
- Field of a long straight wire
- Same direction
- Opposite directions
- Memory aid
- Equal forces
Part 1 of 7Wires interact through their fields
1Field of a current
- Field of a current every current-carrying wire creates a magnetic field around itself
- The field direction follows the right-hand grip rule.
2Second wire
- Second wire it carries current in that field, so it feels a force (D.3.1)
3Third law
- Third law the first wire feels an equal and opposite force from the field of the second
- The wires interact without touching.
4Field of a long straight wire
- Field of a long straight wire concentric circles with B = μ0I / (2πr)
- μ0 = 4π × 10−7 T m A−1 is the permeability of free space.
- I is the current in A and r the perpendicular distance in m.
- The field falls as 1/r.
Part 2 of 7Attraction or repulsion
Same direction
- Same direction parallel currents attract, because the field lines between the wires cancel
- Forces point towards each other.
Opposite directions
- Opposite directions antiparallel currents repel, because the fields between the wires reinforce
- Forces point away from each other.
Memory aid
- Memory aid like currents attract, the opposite of electric charges
Cables
- Cables the two conductors of a heavy-current lead carry antiparallel currents
- A short circuit gives a very large repelling force, so heavy cables are clamped firmly.
Part 3 of 7Force per unit length
Equation
- F/L = μ0I1I2 / (2πr)
- F/L is the force per metre of wire in N m−1.
- I1 and I2 are the two currents in A.
- r is the separation of the wires in m.
Equal forces
- Equal forces the forces on the two wires are equal and opposite, even if the currents differ
Proportionality
- Proportionality doubling either current doubles the force and doubling the separation halves it
- The relation is inverse, not inverse-square.
Part 4 of 7Deriving the equation
1
The field of wire 2 at wire 1 is B2 = μ0I2/(2πr).
2
This field is perpendicular to wire 1, so sin θ = 1.
3
The force on a length L of wire 1 is F = B2I1L.
4
Divide by L: F/L = B2I1.
5
Substitute B2 to get F/L = μ0I1I2/(2πr).
- Validity
- it strictly applies to very long wires, or short sections near the middle of long wires
Part 5 of 7Definition of the ampere
Historical definition
- 1 A is the constant current that, in two infinitely long parallel wires of negligible cross-section 1 m apart in a vacuum, produces a force of 2 × 10−7 N per metre
Check
- F/L = (4π × 10−7 × 1 × 1)/(2π × 1) = 2 × 10−7 N m−1
Today
- Today the ampere is defined by fixing the value of the elementary charge
- The wire definition still shows how μ0 got its value.
Part 6 of 7Several wires
Several wires
Write the field formula for the first wire.
Write the force formula for the second wire.
State attraction or repulsion and give the reason.
1Three wires or corners
- Three wires or corners work out the force from each neighbour separately and add them as vectors
2Zero-field point, same-direction currents
- Zero-field point, same-direction currents it lies between the wires where μ0I1/(2πr1) = μ0I2/(2πr2)
3Zero-field point, opposite currents
- Zero-field point, opposite currents it lies outside the pair, on the side of the smaller current
4Between antiparallel wires
- Between antiparallel wires the fields reinforce
Part 7 of 7More from the specification
More from the specification
Magnetic Force Between Parallel Current-Carrying Conductors
- Two parallel wires carrying electric currents exert magnetic forces on each other;
- currents flowing in the same direction attract,
- while currents in opposite directions repel, governed by the interaction of each wire's magnetic field with the moving charge carriers in the other.
Charged Particles Moving in a Uniform Magnetic Field
- When a charged particle moves with speed v through a uniform magnetic field B, it experiences a magnetic Lorentz force F = q·v·B·sin θ directed perpendicular to both velocity and field lines,
- (such as a proton or electron)
- causing circular motion.
Deflection of Positive and Negative Particles and Fleming's Rule — By Fleming's left-hand rule, a positively charged proton experiences a force in the direction of conventional current,
- while a negatively charged electron experiences a force in the opposite direction;
- between charged plates, electrostatic forces deflect particles towards the oppositely charged plate.
Uniform
- Same density throughout, so the weight acts at the centre.
Proton
- Positive particle in the nucleus, relative charge +1 and relative mass 1.
Velocity
- Rate of change of displacement.
Density
- Mass per unit volume.
Charge-to-mass ratio
- Q/m, which determines the acceleration in a given field
Field strength
- G = Fg/m.
F = Bqv
What the symbols mean: F = force on the moving charge (N) · B = magnetic flux density (T) · q = charge (C) · v = speed (m s−1)
Key terms
| Term | Meaning |
|---|---|
| Permeability of free space μ₀ | Constant 4π × 10⁻⁷ T m A⁻¹ linking current to field in vacuum. |
| Force per unit length | F/L between two parallel wires, in N m⁻¹. |
| Ampere | SI unit of current; its older definition used the force between wires. |
| Concentric field lines | Circular field lines around a straight current-carrying wire. |
| Antiparallel | Currents in opposite directions, which repel. |
Avoid these mistakes
1
Saying parallel currents in the same direction repel because like repels like.
2
Using the wrong distance in the field formula — r must be the perpendicular distance to the wire creating the field.
3
Forgetting that the forces on the two wires are equal in size, even if the currents are different.
4
Leaving out the 2π in the formula, or confusing F/L with the total force.
5
Doubling the separation but expecting a quarter of the force — the relation is inverse, not inverse-square.
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