Magnetic fields

IB Physics SL· Unit 4: Fields, Topic 3: Magnetic Fields· 15 min read

1. Magnetic Field Basics★★☆☆☆⏱ 4 min

A magnetic field is a force field that exists around magnetic materials and moving electric charges. Unlike electric fields (which act on all charges), magnetic fields only exert a force on moving charges. Field lines are used to visualize fields: they run from north to south outside a magnet, never cross, and closer lines mean a stronger field.

📘 Definition

Magnetic Flux Density

B

A measure of magnetic field strength, defined as force per unit current per unit length on a wire placed perpendicular to the field. SI unit is the tesla (T).

Example:

A strong bar magnet has $B \approx 1$ T near its surface.

B = \frac{F}{Il}

📐 Worked Example

A 0.5 m long wire carrying 2 A current is placed perpendicular to a uniform magnetic field, and experiences a force of 0.4 N. Calculate $B$ .

1
Use the definition of magnetic flux density for a perpendicular wire:
2
$B = \frac{F}{Il}$
3
Substitute the given values: $F = 0.4$ N, $I = 2$ A, $l = 0.5$ m:
4
$B = \frac{0.4}{(2)(0.5)} = 0.4$
5
Final answer with unit: $B = 0.4$ T

2. Magnetic Force on Moving Charges★★★☆☆⏱ 4 min

When a charged particle moves through a magnetic field, it experiences the magnetic component of the Lorentz force. The magnitude of the force depends on the particle's charge, speed, field strength, and the angle between the particle's velocity and the magnetic field.

F = qvB \sin\theta

Where $θ$ is the angle between the velocity vector $v$ and the magnetic flux density vector $B$ . Force is maximum when $θ = 9 0^{\circ}$ ( $sin 9 0^{\circ} = 1$ ) and zero when $θ = 0^{\circ}$ (velocity parallel to field).

📐 Worked Example

An electron moving at $2 \times 1 0^{6}$ m/s enters a uniform 0.1 T magnetic field perpendicular to its velocity. Calculate the magnitude of the force on the electron. ( $e = 1.6 \times 1 0^{- 19}$ C)

1
Velocity is perpendicular to $B$ , so $θ = 9 0^{\circ}$ , $sin 9 0^{\circ} = 1$ , so $F = q v B$ :
2
$F = (1.6 \times 10^{-19})(2 \times 10^6)(0.1)$
3
Calculate the result:
4
$F = 3.2 \times 10^{-14} \text{ N}$
5
Direction is opposite to the right-hand rule result because the electron has negative charge.

3. Force on Current-Carrying Wires★★★☆☆⏱ 3 min

A current in a wire is a flow of moving charges, so the net magnetic force on all individual charges adds up to a total force on the entire wire. The formula for total force is derived directly from the Lorentz force law for individual charges.

F = BIl \sin\theta

Where $I$ is current, $l$ is wire length, and $θ$ is the angle between the current direction and the magnetic field.

✓ Quick check

Test your understanding:

When is the magnetic force on a current-carrying wire in a uniform field equal to zero?
- When current is parallel to $B$
- When current is perpendicular to $B$
- When $B = 0$
- Both A and C
Reveal answer
3 —
Correct! $sin 0^{\circ} = 0$ when current is parallel to $B$ , so $F = 0$ , and $F$ is also zero if there is no magnetic field.

📐 Worked Example

A 1.2 m wire carrying 3 A current is at $3 0^{\circ}$ to a 0.2 T magnetic field. Find the force on the wire.

1
Use the force formula for current-carrying wires:
2
$F = BIl \sin\theta$
3
Substitute values: $sin 3 0^{\circ} = 0.5$
4
$F = (0.2)(3)(1.2)(0.5) = 0.36$
5
Final answer: $F = 0.36$ N, direction perpendicular to both current and $B$ .

4. Magnetic Fields from Currents★★★☆☆⏱ 4 min

All moving charges produce magnetic fields, so any current flowing through a conductor creates a magnetic field around it. The shape and direction of the field depend on the geometry of the conductor.

Straight wire: Concentric circular field lines around the wire, direction given by the right-hand grip rule.
Solenoid (long coil): Uniform magnetic field inside the coil, shape identical to a bar magnet, direction given by right-hand grip rule.
Flat circular coil: Field perpendicular to the plane of the coil at its center.

📘 Definition

Right-Hand Grip Rule

A mnemonic to find the direction of the magnetic field produced by a current-carrying conductor.

Example:

For straight wires: thumb points along current, fingers curl in field direction. For solenoids: fingers curl along current, thumb points to the north end.

📐 Worked Example

A current flows vertically upwards through a straight wire directly in front of you. What is the direction of the magnetic field at a point to the right of the wire?

1
Point the thumb of your right hand upwards, aligned with the current direction.
2
Curl your fingers around the wire to follow the direction of the magnetic field lines.
3
At a point to the right of the wire, your fingers point into the plane of the page.
4
Conclusion: Magnetic field direction is into the page.

5. Common Pitfalls

Wrong move:

Claiming magnetic force acts on a stationary charge in a magnetic field

Why:

Magnetic force depends on velocity: if $v = 0$ , then $F = 0$

Correct move:

Remember magnetic fields only exert force on charges moving relative to the field

Wrong move:

Using the right-hand rule direction directly for negative charges

Why:

The right-hand rule is defined for positive charges; negative charge force is opposite

Correct move:

Always reverse the direction from the right-hand rule for negative charges

Wrong move:

Omitting the $sin θ$ term, assuming $F = B I l$ or $F = q v B$ always

Why:

Force is only maximum when velocity/current is perpendicular to $B$

Correct move:

Always check the angle and include $sin θ$ in your calculation

Wrong move:

Mixing up the right-hand grip rule for straight wires and solenoids

Why:

The rule is applied differently for each conductor geometry

Correct move:

Straight wire: thumb = current, fingers = field. Solenoid: fingers = current, thumb = north pole

6. Quick Reference Cheatsheet

Quantity/Rule	Formula/Description	Notes
Magnetic flux density	$B = \frac{F}{I l}$	Perpendicular wire, unit: T
Force on moving charge	$F = q v B sin θ$	$θ$ = angle $v$ & $B$
Force on current wire	$F = B I l sin θ$	$θ$ = angle $I$ & $B$
Force direction (positive)	Right hand: index = $v$ , middle = $B$ , thumb = $F$	Reverse for negative charges
Straight wire field	Thumb along current, fingers = field direction	Concentric circular field lines
Solenoid field	Fingers along current, thumb = north pole	Uniform field inside solenoid

7. Frequently Asked

How do I find the force direction for negative charges?

Reverse the direction you get from the standard right-hand rule for positive charges, or use your left hand instead of your right hand for negative charges.

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.

2025 · Paper 1
Force on moving proton in B-field
2024 · Paper 2
Solenoid field and force calculation
2023 · Paper 1
Direction of magnetic force on wire

Going deeper

syllabusIB Physics SL 2025 Unit 4 SyllabusOfficial reference

What's Next

Magnetic fields are a core component of electromagnetism, which accounts for roughly 20% of the IB Physics SL exam marks. Mastering the basics here will make it much easier to understand electromagnetic induction, the next key topic in unit 4. You can also deepen your understanding by reviewing the circular motion of charged particles in magnetic fields, a common exam application of this topic. Next, explore the following related topics to build your knowledge.