Force on current-carrying conductor

CIE A-Level Physics· Unit 23: Magnetic fields· 10 min read

1. Origin of the Force★★☆☆☆⏱ 2 min

An electric current in a conductor is a net flow of charged particles (usually electrons in metallic conductors). When the conductor is placed inside an external magnetic field, each moving charged particle experiences an individual magnetic force. The sum of all these individual forces gives the net force on the entire conductor.

📘 Definition

Motor Effect

The phenomenon where a current-carrying conductor placed in a magnetic field experiences a net force, which is the working principle of electric motors.

2. Magnitude of the Force★★★☆☆⏱ 4 min

The magnitude of the force depends on four factors: magnetic flux density $B$ , current $I$ , length of conductor $L$ inside the field, and the angle $h e t a$ between the direction of current and the magnetic field vector.

🔬 Derivation

Goal:

Derive the general force formula for a current-carrying conductor

Starting from:

Force on a single moving charge: $F = q v B sin θ$

1
For a conductor of length $L$ , cross-sectional area $A$ , number density of charge carriers $n$ , total charge carriers = $n A L$
2
Current is defined as $I = n A q v$ , where $v$ is drift velocity of charge carriers
3
Total force = number of charge carriers × force per charge carrier
4
$F = (nAL)(qvB\sin\theta) = (nAqv)LB\sin\theta$
5
Substitute $I = n A q v$ into the equation:
6
$F = BIL\sin\theta$

Result:

This is the general formula for force on any straight current-carrying conductor in a uniform magnetic field.

📐 Worked Example

A straight wire of length 0.5 m carries a current of 3 A, placed in a uniform magnetic field of flux density 0.2 T. The angle between current and magnetic field is 30°. Calculate the force on the wire.

1
List known values: $B = 0.2$ T, $I = 3$ A, $L = 0.5$ m, $θ = 3 0^{\circ}$
2
Use the general force formula $F = B I L sin θ$
3
Substitute values: $F = 0.2 \times 3 \times 0.5 \times sin 3 0^{\circ}$
4
We know $sin 3 0^{\circ} = 0.5$ , so: $F = 0.2 \times 3 \times 0.5 \times 0.5 = 0.15$ N
5
Final answer: Force on the wire is 0.15 N

3. Direction of the Force★★☆☆☆⏱ 3 min

The force is always perpendicular to both the direction of current and the direction of the magnetic field, following the cross product rule $F = I L \times B$ . For exam purposes, we use a simple mnemonic to find the direction.

📐 Worked Example

A horizontal wire carries current from left to right, placed in a magnetic field pointing into the page. Find the direction of the force on the wire.

1
Align your left hand: point your first finger into the page (matches magnetic field direction)
2
Point your second finger to the right (matches current direction left to right)
3
Your thumb will point upwards, which is the direction of the force on the wire

✓ Quick check

Test your understanding:

A current-carrying wire is parallel to a uniform magnetic field. What is the force on the wire?
- Equal to $B I L$
- Zero
- Half $B I L$
- Cannot be calculated
Reveal answer
1 —
When the wire is parallel to the field, $θ = 0^{\circ}$ , so $sin θ = 0$ , meaning force is zero.

4. Common Pitfalls

Wrong move:

Using Fleming's Right Hand Rule instead of Left Hand Rule

Why:

Right Hand Rule is for electromagnetic induction (generators), not for finding force on existing current (motor effect)

Correct move:

Always use Left Hand Rule to find the direction of force on a current-carrying conductor

Wrong move:

Using $F = B I L$ for all angles, omitting $sin θ$

Why:

$F = B I L$ only works when the conductor is perpendicular to the magnetic field. It gives the wrong magnitude for any other angle

Correct move:

Always use the general formula $F = B I L sin θ$ , and only simplify to $F = B I L$ when you confirm the conductor is perpendicular

Wrong move:

Using the angle between conductor and force instead of current and field

Why:

$θ$ in the formula is defined specifically as the angle between current direction and magnetic field direction, so using the wrong angle gives an incorrect result

Correct move:

Always first identify the direction of current and direction of magnetic field, then calculate the angle between these two vectors

Wrong move:

Swapping the fingers for current and field in Fleming's Left Hand Rule

Why:

Swapping these gives the opposite direction of force, leading to wrong answers in multiple choice and written questions

Correct move:

Remember the mnemonic: First = Field, seCond = Current, THumb = Thrust to avoid mixing up fingers

5. Quick Reference Cheatsheet

Concept	Formula / Rule	Key Notes
General force magnitude	$F = B I L sin θ$	$θ$ = angle between current and field
Conductor perpendicular to field	$F = B I L$	Maximum possible force
Conductor parallel to field	$F = 0$	No force acts on the conductor
Fleming's Left Hand	First=Field, Second=Current, Thumb=Force	Use for direction of force

6. Frequently Asked

Does reversing current reverse the direction of force?

Yes, force direction is dependent on both current and magnetic field direction. Reversing either reverses force direction; reversing both leaves force unchanged.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · 1
Direction of force on a wire
2022 · 2
Calculate force on inclined wire
2021 · 4
Force on suspended current-carrying wire

Going deeper

syllabusCIE 9702 Latest SyllabusCheck for latest topic requirements

What's Next

The force on a current-carrying conductor is a foundational concept for all electromagnetism topics in CIE A-Level Physics. This effect is the basis of electric motors, loudspeakers, and many other electromagnetic devices that are common in exam questions. It also leads directly to the force between parallel current-carrying conductors, which is used to define the SI unit of current, the ampere. Mastering this topic will make it much easier to understand electromagnetic induction, the next major core concept in magnetic fields.