Force And Torque Due To Magnetic Field

Force and Torque Due to Magnetic Field - Introduction

Introduction to magnetic fields
Definition of force and torque
Magnetic force on a charged particle in a magnetic field
Determining the direction of magnetic force
Equation for magnetic force
Magnetic force on a current-carrying conductor
Torque on a current loop in a magnetic field
Magnetic field strength and magnetic permeability
Application of magnetic force in everyday life

Slide 11:

Magnetic Field of a Straight Current-Carrying Conductor

A current-carrying conductor produces a magnetic field around it
The magnetic field lines form circular loops around the conductor
The direction of the magnetic field can be determined using the right-hand rule
The strength of the magnetic field depends on the magnitude of the current and the distance from the conductor
The magnetic field decreases as the distance from the conductor increases

Slide 12:

Force on a Current-Carrying Conductor in a Magnetic Field

When a current-carrying conductor is placed in a magnetic field, it experiences a force
The force on the conductor is perpendicular to both the magnetic field and the direction of the current
The magnitude of the force can be determined using the formula: F = BIL
B is the magnetic field strength, I is the current, and L is the length of the conductor in the magnetic field

Slide 13:

Direction of the Force on a Current-Carrying Conductor

The direction of the force can be determined using Fleming’s left-hand rule
We can use the thumb, index finger, and middle finger to represent the direction of the magnetic field, current, and force respectively
For a straight current-carrying conductor, the force is perpendicular to both the field and current, following the right-hand rule

Slide 14:

Examples: Force on a Current-Carrying Conductor

A wire carrying a current of 4 A is placed in a magnetic field of 0.6 T. What is the force experienced by the wire?
Solution: F = BIL = (0.6 T)(4 A)(L)
The length of the wire should be provided in order to find the force

Slide 15:

Torque on a Current Loop in a Magnetic Field

A current-carrying loop placed in a magnetic field experiences a torque
The torque on the loop can be determined using the formula: τ = BIAN
B is the magnetic field strength, I is the current, A is the area of the loop, and N is the number of turns in the loop

Slide 16:

Direction of the Torque on a Current Loop

The direction of the torque can be determined using the right-hand rule
We can use the thumb, index finger, and middle finger to represent the direction of the magnetic field, current, and torque respectively
The torque will tend to align the loop with the magnetic field

Slide 17:

Examples: Torque on a Current Loop

A circular loop with a radius of 0.2 m and carrying a current of 2 A is placed in a magnetic field of 0.8 T. What is the torque experienced by the loop?
Solution: τ = BIAN = (0.8 T)(2 A)(π(0.2 m)^2)
The number of turns in the loop should be provided in order to find the torque

Slide 18:

Magnetic Field Due to a Solenoid

A solenoid is a coil of wire that produces a magnetic field when a current passes through it
The magnetic field inside a solenoid is strong and uniform
The direction of the magnetic field inside a solenoid can be determined by the right-hand rule
The strength of the magnetic field inside a solenoid depends on the number of turns, the current, and the length of the solenoid

Slide 19:

Magnetic Field Due to a Bar Magnet

A bar magnet has two poles: a north pole and a south pole
The magnetic field lines emerge from the north pole and enter the south pole
The magnetic field is strongest near the poles and weaker further away
The direction of the magnetic field is from the north pole to the south pole inside the magnet

Slide 20:

Application of Magnetic Forces and Torque

Maglev trains: Magnetic forces are used to levitate and propel trains without using wheels
Electric motors: Torque on the rotor due to magnetic fields is used to convert electrical energy into mechanical energy
Loudspeakers: Magnetic forces on a coil in a magnetic field are used to produce sound vibrations
Magnetic resonance imaging (MRI): Magnetic fields and forces are used to create detailed images of the body for medical diagnosis

Slide 21:

Applications of Magnetic Fields

Electric generators: Conversion of mechanical energy into electrical energy through magnetic fields
Transformers: Changing the voltage of an alternating current using magnetic induction
Magnetic locks: Security systems that use magnetic fields to secure doors
Magnetic compasses: Navigational tools that use the Earth’s magnetic field to determine direction
Magnetic levitation vehicles: High-speed transportation systems that rely on magnetic fields to lift and propel vehicles

Slide 22:

Force and Torque Equations

The formula for magnetic force F on a charged particle is F = qvB
The formula for torque τ on a current-carrying loop is τ = NABI sinθ
The equation for magnetic field strength B inside a solenoid is B = μ₀nI
The equation for magnetic field strength B around a current-carrying straight wire is B = μ₀I/(2πr)
The equation for magnetic field strength B around a bar magnet is B = μ₀m/(4πr³)

Slide 23:

Magnetic Permeability

Magnetic permeability (μ) of a material describes its ability to support the formation of magnetic fields
Vacuum permeability (μ₀) is the permeability of free space and has a value of 4π x 10⁻⁷ Tm/A
Relative permeability (μᵣ) is the ratio of a material’s permeability to the vacuum permeability
μ = μ₀μᵣ
Materials with high permeability are used in the construction of magnetic cores for transformers and electromagnets

Slide 24:

Magnetic Field Strength vs. Magnetic Flux Density

Magnetic field strength (H) is the applied magnetic field created by a current-carrying conductor or a solenoid
Measured in units of amperes per meter (A/m)
Magnetic flux density (B) is the actual magnetic field that exists within a given material
Measured in units of teslas (T)
B = μ₀H

Slide 25:

Magnetic Field Mapping

Magnetic field mapping is a technique used to visualize the shape and strength of magnetic fields
Iron filings or compasses are used to trace the field lines
The spacing between field lines represents the strength of the magnetic field
Field lines never cross each other and form closed loops
Mapping magnetic fields is important in understanding the behavior of magnets and magnetic materials

Slide 26:

Magnetic Force on a Moving Charge

When a charged particle moves through a magnetic field, it experiences a magnetic force
The force is always perpendicular to both the velocity and the magnetic field
The direction of the force can be determined using the left-hand rule
The magnitude of the force is given by F = qvB sinθ
The force can change the direction of the particle’s motion but not its speed

Slide 27:

Magnetic Field Due to Current in a Wire

Ampere’s law states that the magnetic field around a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire
The direction of the magnetic field can be determined using the right-hand grip rule
The magnetic field forms concentric circles around the wire
The field strength decreases as the distance from the wire increases

Slide 28:

Magnetic Field Inside a Toroid

A toroid is a donut-shaped object with a coil of wire wrapped around it
The magnetic field inside a toroid is strong and uniform
The field lines inside the toroid are concentric circles
The direction of the magnetic field can be determined using the right-hand grip rule
The strength of the magnetic field inside a toroid depends on the number of turns, the current, and the radius of the toroid

Slide 29:

Magnetic Field Strength and Magnetic Flux

Magnetic flux (Φ) is a measure of the total magnetic field passing through a given area
Magnetic field strength (B) and area (A) are related to magnetic flux through the equation Φ = B.A cosθ
The magnetic flux is maximum when the field lines are perpendicular to the area (θ = 0° or 180°)
The magnetic flux is minimum when the field lines are parallel to the area (θ = 90°)

Slide 30:

Magnetic Field Induced by a Changing Magnetic Flux

When the magnetic flux through a coil changes, an electromotive force (emf) is induced
The magnitude of the induced emf is given by Faraday’s Law of electromagnetic induction: emf = -dΦ/dt
Lenz’s Law states that the direction of the induced current will oppose the change in magnetic flux
This phenomenon is the basis for electric generators and transformers
Examples of applications of electromagnetic induction include power generation, wireless charging, and induction heating.