Force on a current-carrying conductor

General physics

Magnetic Force on Current-Carrying Conductors — Physics Lesson

🎯 Learning Objectives

Learning Objectives

Understand that a force might act on a current-carrying conductor placed in a magnetic field
Recall and use the equation F = BIL sin θ, with directions as interpreted by Fleming’s left-hand rule
Analyze the factors affecting the magnitude of magnetic force on conductors
Apply Fleming’s left-hand rule to determine force directions in various scenarios
Solve problems involving magnetic forces on current-carrying wires
Understand practical applications of magnetic forces in electric motors and other devices

🗣️ Language Objectives

Language Objectives

Use precise scientific terminology related to magnetism and electric current
Explain the relationship between magnetic field, current, and force using appropriate physics vocabulary
Describe Fleming’s left-hand rule using clear directional language
Communicate problem-solving strategies for magnetic force calculations effectively
Write mathematical expressions and interpret physics equations accurately
Discuss real-world applications of magnetic forces using technical language

📝 Key Terms

Key Terms

English Term	Russian Translation	Kazakh Translation
Magnetic Force	Магнитная сила	Магниттік күш
Current-carrying Conductor	Проводник с током	Токты өткізетін өткізгіш
Magnetic Field	Магнитное поле	Магнит өрісі
Fleming’s Left-hand Rule	Правило левой руки Флеминга	Флемингтің сол қол ережесі
Magnetic Flux Density	Магнитная индукция	Магниттік индукция
Electric Current	Электрический ток	Электр тогы
Perpendicular	Перпендикулярный	Перпендикуляр
Tesla (T)	Тесла	Тесла

🃏 Topic Flashcards

Interactive Flashcards

Practice with these flashcards to memorize key concepts about magnetic forces on current-carrying conductors.

📚 Glossary

Glossary

Magnetic Force: The force experienced by a current-carrying conductor when placed in a magnetic field. This force is perpendicular to both the direction of current and the magnetic field lines.
Translation
Russian: Магнитная сила — сила, испытываемая проводником с током при помещении в магнитное поле. Эта сила перпендикулярна как направлению тока, так и линиям магнитного поля.
Kazakh: Магниттік күш — магнит өрісіне орналастырылған токты өткізетін өткізгіштің сезінетін күші. Бұл күш ток бағытына да, магнит өрісінің сызықтарына да перпендикуляр.
Current-carrying Conductor: Any material or wire through which electric current flows. When placed in a magnetic field, these conductors experience a magnetic force due to the interaction between the current and the magnetic field.
Translation
Russian: Проводник с током — любой материал или провод, через который протекает электрический ток. При помещении в магнитное поле эти проводники испытывают магнитную силу из-за взаимодействия между током и магнитным полем.
Kazakh: Токты өткізетін өткізгіш — электр тогы ағатын кез келген материал немесе сым. Магнит өрісіне орналастырылғанда, бұл өткізгіштер ток пен магнит өрісінің арасындағы өзара әрекеттесу салдарынан магниттік күш сезінеді.
Magnetic Field (B): A region around a magnet or current-carrying conductor where magnetic forces can be detected. Measured in Tesla (T), it represents the magnetic flux density at any point in space.
Translation
Russian: Магнитное поле — область вокруг магнита или проводника с током, где могут быть обнаружены магнитные силы. Измеряется в Теслах (Т), представляет магнитную индукцию в любой точке пространства.
Kazakh: Магнит өрісі — магниттік күштерді анықтауға болатын магнит немесе токты өткізетін өткізгіштің айналасындағы аймақ. Тесламен (Т) өлшенеді, кеңістіктің кез келген нүктесіндегі магниттік индукцияны білдіреді.
Fleming’s Left-hand Rule: A memory aid used to determine the direction of force on a current-carrying conductor in a magnetic field. The thumb, first finger, and middle finger of the left hand represent Force, Field, and Current respectively, all at right angles to each other.
Translation
Russian: Правило левой руки Флеминга — мнемоническое правило для определения направления силы, действующей на проводник с током в магнитном поле. Большой палец, указательный и средний пальцы левой руки представляют Силу, Поле и Ток соответственно, все под прямыми углами друг к другу.
Kazakh: Флемингтің сол қол ережесі — магнит өрісіндегі токты өткізетін өткізгішке әсер ететін күштің бағытын анықтау үшін қолданылатын есте сақтау ережесі. Сол қолдың бас бармағы, сұқ саусағы және орта саусағы сәйкесінше Күшті, Өрісті және Токты білдіреді, барлығы бір-біріне тік бұрыш жасайды.
Magnetic Flux Density (B): The strength of a magnetic field at a particular point, measured in Tesla (T). It represents the number of magnetic field lines passing through a unit area perpendicular to the field direction.
Translation
Russian: Магнитная индукция — сила магнитного поля в определенной точке, измеряется в Теслах (Т). Представляет количество линий магнитного поля, проходящих через единицу площади, перпендикулярной направлению поля.
Kazakh: Магниттік индукция — белгілі бір нүктедегі магнит өрісінің күші, Тесламен (Т) өлшенеді. Өріс бағытына перпендикуляр бірлік ауданнан өтетін магнит өрісі сызықтарының санын білдіреді.
Electric Current (I): The flow of electric charge through a conductor, measured in Amperes (A). In the context of magnetic forces, it’s the current flowing through the conductor that interacts with the magnetic field.
Translation
Russian: Электрический ток — поток электрического заряда через проводник, измеряется в Амперах (А). В контексте магнитных сил это ток, протекающий через проводник, который взаимодействует с магнитным полем.
Kazakh: Электр тогы — өткізгіш арқылы электр зарядының ағыны, Амперпен (А) өлшенеді. Магниттік күштер контекстінде бұл магнит өрісімен әрекеттесетін өткізгіш арқылы ағатын ток.
Length of Conductor (L): The length of the current-carrying conductor that is within the magnetic field. Only this portion of the conductor experiences the magnetic force, measured in meters (m).
Translation
Russian: Длина проводника — длина проводника с током, находящегося в магнитном поле. Только эта часть проводника испытывает магнитную силу, измеряется в метрах (м).
Kazakh: Өткізгіштің ұзындығы — магнит өрісінде орналасқан токты өткізетін өткізгіштің ұзындығы. Өткізгіштің тек осы бөлігі магниттік күш сезінеді, метрмен (м) өлшенеді.
Angle θ (Theta): The angle between the direction of current flow and the direction of the magnetic field. The magnetic force is maximum when θ = 90° (perpendicular) and zero when θ = 0° (parallel).
Translation
Russian: Угол θ (тета) — угол между направлением течения тока и направлением магнитного поля. Магнитная сила максимальна при θ = 90° (перпендикулярно) и равна нулю при θ = 0° (параллельно).
Kazakh: θ (тета) бұрышы — ток ағымының бағыты мен магнит өрісінің бағыты арасындағы бұрыш. Магниттік күш θ = 90° (перпендикуляр) болғанда максималды, ал θ = 0° (параллель) болғанда нөлге тең.

📖 Theory: Magnetic Force on Current-Carrying Conductors

Theory: Understanding Magnetic Forces and Fleming’s Left-Hand Rule

Introduction to Magnetic Forces

When a current-carrying conductor is placed in a magnetic field, it experiences a force. This phenomenon forms the basis of many electrical devices including electric motors, loudspeakers, and electromagnetic brakes.

Kazakh Translation

Токты өткізетін өткізгіш магнит өрісіне орналастырылғанда, ол күш сезінеді. Бұл құбылыс электр қозғалтқыштары, дауыскөтергіштер және электромагниттік тежегіштер сияқты көптеген электр құрылғыларының негізін құрайды.

Magnetic force on current-carrying conductor

Diagram showing magnetic force acting on a current-carrying conductor in a magnetic field

The Fundamental Equation

The magnitude of the magnetic force on a current-carrying conductor is given by:

F = BIL sin θ

Where:

Symbol	Quantity	Unit	Description
F	Magnetic Force	Newton (N)	Force experienced by the conductor
B	Magnetic Flux Density	Tesla (T)	Strength of magnetic field
I	Electric Current	Ampere (A)	Current flowing through conductor
L	Length	Meter (m)	Length of conductor in magnetic field
θ	Angle	Degrees (°) or Radians	Angle between current and field

Kazakh Translation

F — өткізгіш сезінетін күш, B — магнит өрісінің күші, I — өткізгіш арқылы ағатын ток, L — магнит өрісіндегі өткізгіштің ұзындығы, θ — ток пен өріс арасындағы бұрыш.

Understanding the sin θ Factor

The sin θ factor is crucial for understanding when maximum and minimum forces occur:

Angle θ	sin θ	Force Magnitude	Description
0°	0	F = 0	Current parallel to field — no force
30°	0.5	F = 0.5 BIL	Half maximum force
60°	0.866	F = 0.866 BIL	Strong force
90°	1	F = BIL	Maximum force — perpendicular
180°	0	F = 0	Current antiparallel to field — no force

Graph showing how magnetic force varies with the angle between current and magnetic field

Fleming’s Left-Hand Rule

To determine the direction of the magnetic force, we use Fleming’s left-hand rule:

Kazakh Translation

Магниттік күштің бағытын анықтау үшін біз Флемингтің сол қол ережесін қолданамыз.

Fleming’s Left-Hand Rule Steps:

Finger	Represents	Direction	Memory Aid
First finger (Index)	Magnetic Field (B)	North → South	Field
Middle finger	Current (I)	Positive → Negative	Current
Thumb	Force (F)	Direction of force	Force

Illustration of Fleming’s left-hand rule showing finger positions for Field, Current, and Force

Physical Explanation

The magnetic force arises from the interaction between the magnetic field of the current and the external magnetic field. Moving charges (current) create their own magnetic field, which interacts with the external field, resulting in a net force.

Kazakh Translation

Магниттік күш токтың магнит өрісі мен сыртқы магнит өрісінің арасындағы өзара әрекеттесуден туындайды. Қозғалатын зарядтар (ток) өзіндік магнит өрісін жасайды, ол сыртқы өріспен әрекеттесіп, нәтижелік күш тудырады.

Practical Applications

Understanding magnetic forces on current-carrying conductors is essential for many technologies:

Application	How It Works	Key Principle
Electric Motors	Current-carrying coils in magnetic field rotate	Continuous force creates rotation
Loudspeakers	Current variations move cone back and forth	Force proportional to current
Maglev Trains	Magnetic forces provide propulsion and levitation	Contactless force transmission
Circuit Breakers	High current creates force to open contacts	Force increases with current

Practice Questions

Question 1 (Easy):

A straight wire carrying a current of 5.0 A is placed perpendicular to a uniform magnetic field of 0.2 T. If the length of wire in the field is 0.3 m, calculate the magnetic force on the wire.

Answer

Given: I = 5.0 A, B = 0.2 T, L = 0.3 m, θ = 90° (perpendicular)
Using F = BIL sin θ
F = 0.2 × 5.0 × 0.3 × sin(90°)
F = 0.2 × 5.0 × 0.3 × 1
F = 0.3 N
The magnetic force on the wire is 0.3 N.

Question 2 (Medium):

A 20 cm long conductor carries a current of 8.0 A at an angle of 30° to a magnetic field of strength 0.15 T. Calculate the magnetic force and determine its direction using Fleming’s left-hand rule.

Answer

Given: L = 20 cm = 0.20 m, I = 8.0 A, θ = 30°, B = 0.15 T
Using F = BIL sin θ
F = 0.15 × 8.0 × 0.20 × sin(30°)
F = 0.15 × 8.0 × 0.20 × 0.5
F = 0.12 N

Direction: Using Fleming’s left-hand rule:
— First finger: Direction of magnetic field
— Middle finger: Direction of current
— Thumb: Shows force direction (perpendicular to both field and current)

Question 3 (Medium):

A horizontal wire carries a current of 12 A from east to west. It is placed in a vertical magnetic field of 0.08 T pointing downward. What is the magnitude and direction of the magnetic force per unit length of the wire?

Answer

Given: I = 12 A (east to west), B = 0.08 T (downward), θ = 90°
Force per unit length = F/L = BI sin θ
F/L = 0.08 × 12 × sin(90°) = 0.96 N/m

Direction using Fleming’s left-hand rule:
— First finger: Downward (magnetic field)
— Middle finger: East to west (current)
— Thumb: North direction (force)

The force is 0.96 N/m directed northward.

Question 4 (Critical Thinking):

Design a simple electric motor using the principles of magnetic force on current-carrying conductors. Explain how you would ensure continuous rotation and discuss the factors that would affect the motor’s torque and speed.

Answer

Basic Motor Design:
1. Components needed:
— Rectangular current-carrying coil (rotor)
— Permanent magnets or electromagnets (stator)
— Commutator and brushes for current reversal
— Power source

2. Ensuring continuous rotation:
— Use commutator to reverse current direction every half rotation
— This ensures force always acts in same rotational direction
— Multiple coils offset by angles for smoother rotation

3. Torque factors:
— Magnetic field strength (B): Stronger field → higher torque
— Current (I): Higher current → higher torque
— Number of turns in coil: More turns → higher torque
— Coil area: Larger area → higher torque

4. Speed factors:
— Supply voltage: Higher voltage → higher speed
— Load resistance: Lower resistance → higher speed
— Magnetic field strength affects both torque and back-EMF

5. Efficiency considerations:
— Minimize friction in bearings
— Optimize magnetic field distribution
— Use proper commutator design to reduce sparking
— Consider cooling for high-power applications

🧠 Memorization Exercises

Exercises on Memorizing Terms

Exercise 1: Formula Components

Complete the magnetic force equation: F = _____ × _____ × _____ × sin _____

The symbol B represents: _______
The symbol I represents: _______
The symbol L represents: _______
The symbol θ represents: _______
When θ = 90°, sin θ = _______

Answer

F = B × I × L × sin θ
1. Magnetic flux density (magnetic field strength)
2. Electric current
3. Length of conductor in magnetic field
4. Angle between current and magnetic field
5. 1 (maximum force)

Exercise 2: Fleming’s Left-Hand Rule Practice

Fill in the correct finger assignments for Fleming’s left-hand rule:

Finger	Represents	Memory Word
Thumb	_______	_______
First finger (Index)	_______	_______
Middle finger	_______	_______

Answer

Thumb: Force (F) — Force
First finger: Magnetic Field (B) — Field
Middle finger: Current (I) — Current

Memory aid: «FBI» — Field, Current (Body), Force

Exercise 3: Units and Measurements

Match each quantity with its correct unit:

Quantities:

Magnetic force
Magnetic flux density
Electric current
Length
Angle

Units:

Tesla (T)
Ampere (A)
Newton (N)
Meter (m)
Degrees (°) or Radians

Answer

1-C: Magnetic force → Newton (N)
2-A: Magnetic flux density → Tesla (T)
3-B: Electric current → Ampere (A)
4-D: Length → Meter (m)
5-E: Angle → Degrees (°) or Radians

📺 Educational Video

Video Tutorial: Magnetic Force on Current-Carrying Conductors

Additional Resources:

🔬 Problem Solving Examples

Worked Examples

Example 1: Force on Straight Conductor

Problem: A straight conductor of length 25 cm carries a current of 6.0 A. It is placed at an angle of 60° to a uniform magnetic field of strength 0.12 T. Calculate the magnetic force on the conductor.

🎤 Audio Solution

Detailed Solution with Pronunciation

Step 1: Identify given values (pronounced: VAL-yooz)

Length L = 25 cm = 0.25 m

Current I = 6.0 A

Angle θ = 60°

Magnetic field B = 0.12 T

Step 2: Apply the formula F = BIL sin θ

F = 0.12 × 6.0 × 0.25 × sin(60°)

F = 0.12 × 6.0 × 0.25 × 0.866

F = 0.18 × 0.866

F = 0.156 N

Step 3: Determine direction using Fleming’s left-hand rule

The force direction is perpendicular to both the current and magnetic field directions

Use your left hand to find the exact direction based on the given orientations

📝 Quick Solution

Brief Solution

Given: L = 0.25 m, I = 6.0 A, θ = 60°, B = 0.12 T

Formula: F = BIL sin θ

F = 0.12 × 6.0 × 0.25 × sin(60°)

F = 0.12 × 6.0 × 0.25 × 0.866

F = 0.156 N

Direction: Use Fleming’s left-hand rule

Answer: F = 0.156 N

Example 2: Current Required for Specific Force

Problem: A horizontal wire of length 40 cm is placed perpendicular to a vertical magnetic field of 0.08 T. What current must flow through the wire to experience an upward magnetic force of 0.24 N?

🎤 Audio Solution

Detailed Solution with Pronunciation

Step 1: List known values

Length L = 40 cm = 0.40 m

Magnetic field B = 0.08 T (vertical)

Required force F = 0.24 N (upward)

Angle θ = 90° (perpendicular)

Step 2: Rearrange formula to solve for current

F = BIL sin θ

I = F / (BL sin θ)

I = 0.24 / (0.08 × 0.40 × sin(90°))

I = 0.24 / (0.08 × 0.40 × 1)

I = 0.24 / 0.032

I = 7.5 A

Step 3: Determine current direction

Using Fleming’s left-hand rule in reverse:

Thumb (force): Upward

First finger (field): Vertical (direction depends on field orientation)

Middle finger (current): Horizontal direction determined by rule

📝 Quick Solution

Brief Solution

Given: L = 0.40 m, B = 0.08 T, F = 0.24 N, θ = 90°

Rearrange formula:

I = F / (BL sin θ)

I = 0.24 / (0.08 × 0.40 × 1)

I = 0.24 / 0.032

I = 7.5 A

Direction: Use Fleming’s left-hand rule to determine current direction for upward force

🔬 Investigation Task

Interactive Simulation

Use this PhET simulation to investigate magnetic forces on current-carrying wires:

Investigation Questions:

How does the magnetic force change when you increase the current in the wire?
What happens to the force when you change the angle between the wire and magnetic field?
How does the direction of current affect the direction of force?
What happens when the current is parallel to the magnetic field lines?

Brief Answers

1. Force increases proportionally with current (F ∝ I) — doubling current doubles the force
2. Force decreases as angle decreases from 90°; maximum at 90°, zero at 0°
3. Reversing current direction reverses force direction (Fleming’s left-hand rule)
4. When current is parallel to field lines (θ = 0°), the force becomes zero

👥 Group/Pair Activity

Collaborative Learning Activity

Work with your partner or group to complete this magnetic force analysis challenge:

Discussion Points:

How do electric motors utilize the principle of magnetic force on current-carrying conductors?
What safety considerations are important when working with high currents in magnetic fields?
How might magnetic levitation systems use these principles?
What factors would an engineer consider when designing electromagnetic devices?

Group Challenge Activities:

Design a simple electromagnetic crane using magnetic force principles
Calculate forces in different motor configurations
Investigate applications in maglev transportation systems
Create demonstrations showing Fleming’s left-hand rule in action

✏️ Individual Assessment

Structured Questions - Individual Work

Question 1 (Analysis):

A rectangular current-carrying loop with dimensions 8.0 cm × 12.0 cm carries a current of 15 A. The loop is placed in a uniform magnetic field of 0.25 T.

Calculate the force on each side of the loop when the plane of the loop is perpendicular to the magnetic field.
Determine the net force on the loop and explain your result.
Calculate the torque on the loop about its center.
How would the forces change if the loop were rotated 45° about an axis parallel to one of its sides?
Explain why electric motors can produce continuous rotation despite the changing forces.

Answer

a) When perpendicular to field:
Force on 8.0 cm sides: F = BIL = 0.25 × 15 × 0.08 = 0.30 N (each)
Force on 12.0 cm sides: F = BIL = 0.25 × 15 × 0.12 = 0.45 N (each)

b) Net force = 0 N. Opposite sides experience equal and opposite forces, so they cancel out.

c) Torque = Force × distance from center
τ = 0.30 N × 0.06 m + 0.30 N × 0.06 m = 0.036 N⋅m

d) At 45°: Forces become F = BIL sin(45°) = 0.707 × original values

e) Motors use commutators to reverse current direction every half rotation, maintaining torque in the same direction

Question 2 (Synthesis):

Design an electromagnetic rail gun system where a conducting projectile is accelerated along two parallel rails by magnetic forces.

Draw a diagram showing the rail gun setup with magnetic field, current, and force directions.
Calculate the acceleration of a 50 g projectile when 10,000 A flows through it in a 0.5 T magnetic field with rail separation of 2.0 cm.
Determine the velocity after traveling 1.0 m if starting from rest.
Analyze the energy considerations and efficiency limitations of such a system.
Compare this system with conventional firearms in terms of projectile velocity potential.

Answer

a) Diagram should show: parallel rails, current flow, perpendicular magnetic field, force direction according to Fleming’s left-hand rule

b) Force: F = BIL = 0.5 × 10,000 × 0.02 = 100 N
Acceleration: a = F/m = 100/(0.05) = 2,000 m/s²

c) Using v² = u² + 2as, where u = 0, a = 2,000 m/s², s = 1.0 m
v² = 0 + 2 × 2,000 × 1.0 = 4,000
v = 63.2 m/s

d) Energy input = I²Rt (resistive losses), energy output = ½mv²
Efficiency limited by resistance, inductance, and field generation costs

e) Rail guns can theoretically achieve much higher velocities (>2000 m/s) but require enormous power supplies

Question 3 (Evaluation):

A proposed magnetic levitation system uses the repulsive force between currents to support a 1000 kg vehicle.

Calculate the current required in a 3.0 m wide conductor to generate enough upward force to support the vehicle in a 0.1 T magnetic field.
Evaluate the practical challenges of maintaining such currents continuously.
Analyze alternative approaches using superconducting magnets or electromagnetic induction.
Compare the energy requirements with other transportation methods.
Assess the safety implications of high magnetic fields and currents for passengers and equipment.

Answer

a) Required force = weight = mg = 1000 × 9.8 = 9800 N
Using F = BIL: I = F/(BL) = 9800/(0.1 × 3.0) = 32,667 A

b) Challenges: Enormous power consumption, resistive heating, conductor damage, power supply complexity

c) Superconductors eliminate resistance losses; electromagnetic induction (like maglev trains) uses changing fields for levitation and propulsion

d) Energy per km much higher than conventional transport due to power generation and cooling requirements

e) Safety concerns: strong magnetic fields affect pacemakers, electronics; high currents pose electrocution risks; require extensive shielding

Question 4 (Critical Thinking):

Investigate the role of magnetic forces in plasma confinement systems used in fusion reactors.

Explain how magnetic fields can exert forces on moving charged particles (plasma).
Design a conceptual magnetic confinement system to contain high-temperature plasma in a torus shape.
Calculate the magnetic field strength required to confine particles with kinetic energy of 10 keV moving at 10⁶ m/s in a 1 m radius curve.
Analyze the challenges of maintaining stable plasma confinement.
Evaluate the potential of magnetic confinement fusion as a future energy source.

Answer

a) Moving charges constitute current;