Magnetic Fields, Field Lines, and Force

Lesson 1 of 3: Magnetism

In this lesson:

• Describe magnetic fields and draw field line diagrams
• Apply the right-hand rule for force on charges and wires
• Calculate and

Learning Objectives for This Lesson

By the end, you will:

1. Describe magnetic field sources and lines
2. Draw and interpret magnetic field line diagrams
3. Apply the right-hand rule for force direction
4. Calculate force on a moving charge:
5. Calculate force on a current-carrying wire:

Iron Filings Reveal the Field

Magnetic field lines appear wherever iron filings align.

Magnetic Field B — The Basics

• is a vector field — magnitude and direction at every point in space
• SI unit: tesla (T) = kg/(A·s²)
• Reference values:
  • Earth's field: T
  • Strong bar magnet: T
  • MRI machine: 1–3 T

Sources of Magnetic Fields Explained

• Permanent magnets: aligned electron spins in magnetic domains
• Moving charges / current: any moving charge creates a B field around it
• Earth's core: liquid iron dynamo → geomagnetic field
• No magnetic monopoles: field lines always form closed loops

Rules for Drawing Magnetic Field Lines

1. Lines emerge from north pole, enter south pole (externally)
2. Inside the magnet: lines run from south to north (closed loops)
3. Direction of is tangent to the field line at each point
4. Density of lines indicates field strength — dense = strong
5. Lines never cross

Field Line Diagrams: Bar Magnet and Wire

Bar magnet: curved loops from N to S · Wire: circular rings wrapping around the wire

The Solenoid as an Electromagnet

• A solenoid (coil of wire with current) produces a uniform field inside
• Outside, field lines resemble a bar magnet
• Solenoid strength controlled by: current magnitude, number of turns, core material

Quick Check: Describe the Magnetic Field

Look at a bar magnet field line diagram.

• Where is the field strongest?
• In which direction does B point at the north pole's face?
• Do field lines ever cross?

Magnetic Force on a Charge:

• = charge (C), = speed (m/s), = field (T), = angle between and
• (parallel to B) → , no force
• (perpendicular to B) → (maximum)

Force Right-Hand Rule (Force RHR)

For a positive charge:

1. Point fingers in the direction of (velocity)
2. Curl fingers toward (field direction)
3. Thumb points in the direction of (force)

For a negative charge: reverse the result (force is opposite).

Force RHR versus Field RHR Compared

Two different right-hand rules — keep setups separate.

Magnetic Force Does No Work

• Magnetic force is always perpendicular to
• Work = ; force velocity means
• →

→ Magnetic force changes direction, not speed

Circular Motion in a Uniform Field

• Force always velocity → force always points toward center
• Result: uniform circular motion at constant speed

Worked Example: Force on a Moving Charge

Given: C, m/s, T,

Worked Example: Finding Force Direction

points East, points Up (North Pole up)

Force RHR (positive charge):

1. Fingers East (along )
2. Curl upward (toward )
3. Thumb points South

→ Force on positive charge is directed South.

Quick Check: Predict the Force Direction

A negative charge moves East. points Up.

What direction is the force?

Apply Force RHR for positive charge, then reverse for negative.

Force on a Current-Carrying Wire:

• = field (T), = current (A), = wire length (m), = angle to
• Force RHR: fingers along , curl toward , thumb =
• Wire = stream of moving charges; summing over length gives

Worked Example: Force on a Wire

Given: A, m, T,

Direction: Apply Force RHR with fingers along , curl toward , thumb gives force direction.

The Motor Principle: Torque from Force

Forces on opposite sides of a current loop point in opposite directions → torque → rotation

Quick Check: Calculate Force on Wire

A horizontal wire carries current to the right. points upward.

What direction is the magnetic force on the wire?

Apply the Force RHR: fingers along current (right), curl toward B (up), thumb = ?

Practice: Mixed Magnetic Force Problems

1. Proton: C, m/s, T,
2. Wire: m, A, T,
3. Same proton, now parallel to

Key Takeaways: Magnetic Fields and Forces

✓ sources: permanent magnets, moving charges, Earth — no magnetic monopoles

✓ — force on moving charge; Force RHR gives direction

✓ — force on current wire; Force RHR with direction

Watch Out: Avoid These Three Errors

E and B fields differ — E acts on static charges; B only acts on moving charges.

Magnetic force never does work — it changes direction, not speed.

Two right-hand rules exist — one for field direction, one for force. Keep them separate.

What Comes Next: Electromagnetic Induction

sec-20-2: Electromagnetic Induction

• What happens when the magnetic field through a loop changes?
• Faraday's Law:
• Lenz's Law: induced current opposes the change
• The foundation of every generator and transformer

Magnetism creates electricity — the most important discovery of the 19th century.