20.2.2Magnetic fields and alternating currents (A Level)

Force on a Current-Carrying Conductor

5 min read 10 parts Lesson 5 of 24 1 quiz

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Lesson summary

20.2.2 Force on a Current-Carrying Conductor — AS PHYSICS 9702 notes: Find the magnitude and direction of the force on a current-carrying wire or coil in a magnetic field.Moving charges — each charge moving across a field feels a sideways force, passed on to the wire as a wholeRe…

What the symbols mean
Applications
Newton's third law
Fleming's left-hand rule
First finger
Second finger

Section 1 of 10Why a current feels a force

Moving charges

Moving charges each charge moving across a field feels a sideways force, passed on to the wire as a whole

Result

F = BIL sin θ
What 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

Applications

Applications electric motors, loudspeakers and moving-coil meters

Newton's third law

Newton's third law the force on the wire equals in magnitude the force the wire exerts on the magnet producing the field

Section 2 of 10Direction of the force

1Fleming's left-hand rule

Fleming's left-hand rule hold the thumb, first finger and second finger at right angles

2First finger

First finger the magnetic Field, from north to south

3Second finger

Second finger the conventional Current, from positive to negative

4Thumb

Thumb the Thrust, the force and direction of motion

5Reversing

Reversing reversing the current or the field reverses the force; reversing both leaves it unchanged

6Notation

Notation a field into the page is drawn as crosses and a field out of the page as dots

Section 3 of 10Calculations

Calculations

At right angles

F = BIL

At angle θ

F = BIL sin θ

Types of problem

Types of problem the force on a known wire, the field needed to balance a weight (BIL = mg),
- or the acceleration of a free wire (F = ma)
  What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s⁻²)

Wire supported by the force

Wire supported by the force for mass per unit length μ, the length cancels, BI = μg, so I = μg/B

Section 4 of 10Force on a rectangular coil

1Opposite forces

Opposite forces current flows one way in one side and the opposite way in the other, so the forces form a couple that turns the coil

2Sides parallel to the field

Sides parallel to the field they feel no force

3d.c. motor

d.c. motor a split-ring commutator reverses the current every half turn so the turning effect continues in the same sense

4N turns

N turns the force on each side is multiplied by N

Section 5 of 10Method for force problems

Method for force problems

Sketch the wire, field and current, marking whether the field is into or out of the page

Decide the angle between wire and field and so whether sin θ is needed

Write F = BIL sin θ with only the length inside the field

If the wire is in equilibrium, equate the magnetic force to the opposing force

If the wire is in equilibrium, equate the magnetic force to the opposing force weight, spring tension or friction

Use Fleming's left-hand rule to state the direction

Section 6 of 10Using ratios

Ratio reasoning
- express the effect of changes as a ratio to avoid recalculating

Section 7 of 10Links

Single charge

F = Bqv sin θ follows by writing I = nAvq

Parallel wires

Parallel wires each creates a field acting on the other, giving the force between conductors

Induction

Induction moving a wire through a field produces an e.m.f., the reverse effect

Section 8 of 10More from the specification

1Lorentz force on current conductors

Lorentz force on current conductors applying Fleming's left-hand rule provides a geometric means to determine force direction on current-carrying wires.

2Field lines

Lines showing the direction and strength of a magnetic field.

3Copper

Metal widely used for electrical wires.

4Perpendicular

At right angles.

Section 9 of 10Key terms

Term	Meaning
Fleming's left-hand rule	gives the direction of force on a current in a magnetic field
Conventional current	the direction of flow of positive charge
Couple	a pair of equal and opposite forces that turns a body
Commutator	a split ring that reverses the current each half turn in a motor
Thrust	the force on the conductor
Moving-coil meter	a meter using the force on a coil in a field

Section 10 of 10Exam technique

Using the whole wire length — only the part in the field counts.

Using the right hand — use the left hand for the force on a current.

Using electron flow as the current direction — use conventional current.

Forgetting that the force is zero when the wire is parallel to the field.