āš” Motor Physics

Magnetic Fields & DC Motor Basics: How Current Powers Motion

Currents Create Magnetic Fields

When electric current flows through a wire, it creates a magnetic field around the wire. This fundamental principle was discovered by Hans Christian Ƙrsted (Danish physicist) in 1820, when he noticed a compass needle deflecting near a current-carrying wire. It linked electricity and magnetism, eventually leading to the development of electric motors, generators, and modern electromagnets!

The Right-Hand Rule

To predict the direction of the magnetic field around a current-carrying wire:

  1. Point your thumb in the direction of current flow (conventional current, + to āˆ’)
  2. Your fingers curl in the direction of the magnetic field lines

šŸ–ļø Right-Hand Rule Demonstration

Straight Wire

Right-Hand Rule for Straight Wire

Thumb = Current direction (I)
Fingers curl = Magnetic field direction (B)

The magnetic field forms circular loops around the wire, getting weaker as you move away.

Current Loop/Coil

Right-Hand Rule for Current Loop

Fingers curl = Current direction (I)
Thumb = Magnetic field through center (B)

This is how motor coils work, current loops create magnetic poles!

šŸ“š More About the Right-Hand Rule ā–¼

Why It Works

    The right hand rule works because electricity and magnetism are naturally "locked" at right angles to each other. Whether energy is flowing through a straight wire or a circular coil, it always creates a magnetic field that loops or pushes in a very specific, predictable direction. The right hand rule uses the shape of your hand to visualize those directions, making the invisible patterns of physics easy to see and predict.

Different Variations

  • Straight wire: Thumb = current, fingers curl = field direction
  • Coil/solenoid: Fingers curl = current, thumb = field through center
  • Force on a wire: Thumb = current, fingers = external field, palm = force direction

Real-World Applications

  • Electric motors: Understanding field direction helps design efficient motors
  • Generators: The same principle works in reverse; moving magnets create current
  • Electromagnets: Predicting pole orientation for lifting magnets, MRI machines
  • Speakers: Current through a coil creates force that moves the speaker cone

šŸ“ Magnetic Field Formulas

These formulas let you calculate the strength of the magnetic field created by electric current. Understanding them helps predict motor performance and design better electromagnets.

Straight Wire

B = Ī¼ā‚€ Ɨ I / (2Ļ€r)

B = field strength (T), I = current (A), r = distance from wire (m)

What it tells us: The magnetic field strength around a straight wire decreases as you move away from the wire (inversely proportional to distance). This is why the field is strongest right next to the wire.

Usage: Calculating field strength at any point near a current-carrying wire, used in cable design and interference calculations.

Solenoid (Coil)

B = Ī¼ā‚€ Ɨ Ī¼įµ£ Ɨ N Ɨ I / L

N = turns, L = length (m), Ī¼įµ£ = relative permeability

What it tells us: The field inside a coil is uniform and directly proportional to current and number of turns. More turns or more current = stronger field. The core material (Ī¼įµ£) can multiply the field by a lot

Usage: This is the key formula for motor design, it tells us how to create strong magnetic fields for maximum torque.

Constants

Ī¼ā‚€ (permeability of free space) = 4Ļ€ Ɨ 10ā»ā· TƗm/A ā‰ˆ 1.257 Ɨ 10ā»ā¶ TƗm/A

This is a fundamental constant of nature, it determines how easily a magnetic field forms in empty space (vacuum).

Ī¼įµ£ (relative permeability): Air ā‰ˆ 1, Ferrite ā‰ˆ 2000, Iron ā‰ˆ 4000

This tells us how much better a material is at supporting magnetic fields compared to empty space. Iron is about 4000 times better than air, which is why motors use iron cores!

šŸ’” Did You Know?

šŸ§² Earth is a Giant Magnet

Earth's magnetic field is created by electric currents in its molten iron outer core ā€” the same concept as in electromagnets! It's about 25-65 microtesla at the surface.

šŸš„ Maglev Trains

Maglev trains use very strong electromagnets to levitate above the track! The Japanese L0 Series can reach speeds over 600 km/h using this technology.

šŸ„ MRI Machines

MRI machines use magnetic fields about 60,000 times stronger than Earth's field to create detailed images of your body ā€” without radiation!

šŸ”Œ The First Electric Motor

Michael Faraday built the first electric motor in 1821, just one year after Ƙrsted discovered that currents create magnetic fields. It was very simple: just a wire dipping into mercury!

From Electricity to Motion

Now that you understand how currents create magnetic fields, let's put this into practice. In an electric motor, the strength of the magnetic field directly affects how much torque (rotational force) the motor can produce.

Why This Calculation Matters

When you're building or selecting a motor for your RC car, you need to understand:

  • Stronger magnetic field = more torque ā€” A motor with a stronger field can push harder against resistance, letting your car accelerate faster or climb hills
  • More current = stronger field ā€” But more current also drains your battery faster and generates more heat
  • Core material matters ā€” Using iron or ferrite instead of air in the motor core multiplies the magnetic field strength by a large factor
  • Trade-offs ā€” More coil turns increase field strength but also increase resistance (meaning more voltage needed)

The simulator below lets you experiment with these variables to see how they affect motor performance.

šŸ”§ Motor & Magnetic Field Simulator

DC Motor Simulator

Magnetic Field Visualization

Motor Speed Estimate

ā‰ˆ 0 RPM

āš ļø Approximate educational estimate only

Results

Magnetic Field Strength: ā€” mT
Formula Used: B = Ī¼ā‚€Ī¼įµ£NI/L
Steady-State Current: ā€” A
Motor Power: ā€” W
View Full Energy Chain ā†’
šŸ“ Show Step-by-Step Work ā–¼

Adjust inputs above to see calculations.

šŸ”„ How DC Motors Work

The Basic Principle

A DC motor converts electrical energy into rotational mechanical energy through the interaction of magnetic fields:

  1. Current flows through the motor's coil (armature)
  2. The current creates a magnetic field around the coil
  3. This field interacts with permanent magnets in the motor housing
  4. The interaction creates a force that causes rotation
  5. A commutator reverses current direction each half-turn to maintain rotation

Note: Detailed torque calculations are more complex. The motor speed is approximately proportional to voltage and inversely related to load.

šŸ“š Technical Note: Back-EMF ā–¼

Back-EMF (Counter Electromotive Force)

As the motor spins, it acts like a generator and produces a voltage that opposes the supply voltage. This is called back-EMF.

  • At startup: No rotation ā†’ no back-EMF ā†’ high current (limited by resistance)
  • At speed: High rotation ā†’ high back-EMF ā†’ reduced current
  • Under load: Motor slows ā†’ less back-EMF ā†’ more current to overcome load

This explains why motors draw more current when starting or under heavy load.

Vsupply = I Ɨ R + Vback-EMF

šŸ“– Worked Examples

Example 1: Solenoid Magnetic Field

Problem: Calculate the magnetic field at the center of a solenoid with 200 turns, length 5 cm, carrying 2 A, with an air core.

Show Solution ā–¼

Given: N = 200, L = 0.05 m, I = 2 A, Ī¼įµ£ = 1

B = Ī¼ā‚€ Ɨ Ī¼įµ£ Ɨ N Ɨ I / L
B = (4Ļ€ Ɨ 10ā»ā·) Ɨ 1 Ɨ 200 Ɨ 2 / 0.05
B = 1.005 Ɨ 10ā»Ā² T = 10.05 mT

Answer: B ā‰ˆ 10 mT

Example 2: Motor Current from Battery Pack

Problem: A 4ƗAA pack (6V) powers a motor with 3Ī© resistance. The batteries have 1.2Ī© total internal resistance. What current flows?

Show Solution ā–¼ 
I = V / (Rmotor + Rinternal)
I = 6 V / (3 Ī© + 1.2 Ī©)
I = 6 / 4.2 = 1.43 A

Answer: I ā‰ˆ 1.4 A

See Complete Energy Chain ā†’