Force And Torque Due To Magnetic Field - Force Between Two Current Carrying Conductors

Slide 1: Force And Torque Due To Magnetic Field - Force between two current carrying conductors

Introduction
Definition of magnetism
Magnetic field and its properties
Force experienced by a current carrying conductor in a magnetic field
Force experienced by two current carrying conductors
Relation between magnetic field, current, and force
Applications of the force between two current carrying conductors
Calculation of force using the formula
Examples of force between two current carrying conductors
Torque experienced by a current carrying loop in a magnetic field

Slide 2: Introduction

Force between two current carrying conductors is an important concept in electromagnetism.
It explains the interaction between two current carrying conductors in a magnetic field.
Understanding this force is crucial in the design and functioning of various electrical devices.
In this lecture, we will explore the force and torque experienced by current carrying conductors in a magnetic field.

Slide 3: Definition of magnetism

Magnetism is a fundamental property of certain materials to attract or repel other materials.
Magnets have two poles - North (N) and South (S).
Like poles repel each other, while unlike poles attract each other.
Magnetic field lines emerge from the North pole and converge at the South pole of a magnet.
Magnetic field lines are a representation of the direction of the magnetic force at different points in space.

Slide 4: Magnetic field and its properties

Magnetic field is a region in which a magnetic force can be experienced.
It is represented by magnetic field lines that indicate the direction and strength of the field.
The magnetic field is a vector quantity, meaning it has both magnitude and direction.
Magnetic field lines never intersect each other.
The strength of the magnetic field is proportional to the closeness of the field lines.

Slide 5: Force experienced by a current carrying conductor in a magnetic field

When a current-carrying conductor is placed in a magnetic field, it experiences a force.
The direction of the force is given by Fleming’s left-hand rule.
The magnitude of the force is given by the formula F = BIL, where F is the force, B is the magnetic field, I is the current, and L is the length of the conductor in the magnetic field.
The force is perpendicular to both the magnetic field and the current direction.

Slide 6: Force experienced by two current carrying conductors

When two current-carrying conductors are placed near each other, they experience a force due to the interaction between their magnetic fields.
The force between the conductors depends on the direction and magnitude of the currents in the conductors.
The force is attractive when the currents are in the same direction and repulsive when the currents are in opposite directions.
The force between two parallel conductors is given by the equation F = (μ₀I₁I₂L)/(2πd), where μ₀ is the permeability of free space, I₁ and I₂ are the currents, L is the length of the conductors, and d is the distance between them.

Slide 7: Relation between magnetic field, current, and force

The force experienced by a current-carrying conductor in a magnetic field is directly proportional to the magnetic field strength.
The force is also directly proportional to the current flowing through the conductor.
The force is inversely proportional to the length of the conductor in the magnetic field.
This relationship is described by the equation F = BIL.

Slide 8: Applications of the force between two current carrying conductors

The force between two current carrying conductors is utilized in various electrical devices.
It is used in electric motors to convert electrical energy into mechanical energy.
It is employed in electromagnets, solenoids, and relays.
The force helps in the operation of loudspeakers and magnetic levitation systems.
The force is essential in transformers for energy transfer between primary and secondary coils.

Slide 9: Calculation of force using the formula

To calculate the force between two current carrying conductors, follow these steps:
1. Determine the values of the magnetic field (B), current (I₁ and I₂), length (L), and distance (d).
2. Substitute the values in the formula F = (μ₀I₁I₂L)/(2πd).
3. Calculate the force using the given formula.
4. Pay attention to the direction of the force based on the direction of the currents.

Slide 10: Examples of force between two current carrying conductors

Example 1: Two parallel wires carrying currents of 2A and 3A are separated by a distance of 0.5m. Calculate the force experienced by each wire.
Example 2: A circular loop of radius 0.1m carries a current of 4A. It is placed in a magnetic field of 0.5T. Find the force experienced by the loop.
Example 3: Two wires carry currents of 5A and 8A in the same direction. If the wires are 2m long and located 0.1m apart, determine the force between them.
Example 4: Two wires carry currents of 6A and 4A in opposite directions. If they are 1.5m long and positioned 0.2m apart, what is the force between them?
Example 5: Calculate the force between two parallel wires carrying currents of 10A each, separated by a distance of 0.3m.

Slide 11:

Torque experienced by a current carrying loop in a magnetic field
- Torque is the rotational counterpart of force.
- When a current-carrying loop is placed in a magnetic field, it experiences a torque due to the interaction between the magnetic field and the loop.
- The torque is given by the equation τ = BILsinθ, where τ is the torque, B is the magnetic field, I is the current, L is the length of the loop, and θ is the angle between the magnetic field and the normal to the loop.
- The torque tends to align the loop with the magnetic field.
- The direction of the torque is given by the right-hand rule.

Slide 12:

Magnetic field strength in terms of number of turns and current in a loop
- When a loop of wire carrying current is formed into a coil with multiple turns, the magnetic field becomes stronger.
- The magnetic field strength at the center of the coil is directly proportional to the number of turns in the coil and the current passing through it.
- The relationship is expressed as B = (μ₀nI), where B is the magnetic field strength, μ₀ is the permeability of free space, n is the number of turns, and I is the current.

Slide 13:

Magnetic field due to a straight current carrying conductor
- The magnetic field produced by a straight current-carrying conductor is perpendicular to the conductor and follows a circular path around it.
- The magnetic field strength decreases with increasing distance from the conductor.
- The formula to calculate the magnetic field B at a distance r from the conductor is given by B = (μ₀I)/(2πr), where μ₀ is the permeability of free space and I is the current.

Slide 14:

Magnetic field due to a circular loop
- The magnetic field produced by a circular loop of radius R is strongest at its center.
- The magnetic field strength at the center of the loop is given by B = (μ₀I)/(2R), where μ₀ is the permeability of free space and I is the current.
- The direction of the magnetic field is perpendicular to the plane of the loop.

Slide 15:

Force between a straight current carrying conductor and a magnetic field
- When a straight current-carrying conductor is placed in a magnetic field, it experiences a force.
- The force is given by the equation F = BIL, where F is the force, B is the magnetic field, I is the current, and L is the length of the conductor in the magnetic field.
- The force is perpendicular to both the magnetic field and the current direction.
- The direction of the force is determined by Fleming’s left-hand rule.

Slide 16:

Force and torque on a current carrying coil in a magnetic field
- A current-carrying coil experiences both force and torque when placed in a magnetic field.
- The total force acting on the coil is the vector sum of the forces acting on each side of the coil.
- The torque experienced by the coil is the product of the force and the perpendicular distance between the force and the axis of rotation.

Slide 17:

Electromagnetic induction
- Electromagnetic induction is the process of generating an electromotive force (emf) in a conductor due to a change in magnetic field.
- This phenomenon was discovered by Michael Faraday.
- According to Faraday’s law of electromagnetic induction, the magnitude of the induced emf is directly proportional to the rate of change of magnetic flux through the loop of wire.
- The induced emf can be calculated using the formula emf = -N(dΦ/dt), where emf is the electromotive force, N is the number of turns in the coil, and (dΦ/dt) is the rate of change of magnetic flux.

Slide 18:

Lenz’s law
- Lenz’s law is a consequence of the law of conservation of energy.
- Lenz’s law states that the direction of the induced current is such that it opposes the change producing it.
- The negative sign in Faraday’s law of electromagnetic induction indicates that the induced current and the change in magnetic field have opposite directions.
- Lenz’s law ensures that the energy used to generate the induced current comes from the external source and not from the magnetic field itself.

Slide 19:

Applications of electromagnetic induction
- Electromagnetic induction has numerous practical applications.
- It is used in generators to convert mechanical energy into electrical energy.
- Transformers use electromagnetic induction to transfer electrical energy between two or more coils.
- Induction cooktops generate heat in pans by using an alternating magnetic field.
- Magnetic levitation trains (maglev) use electromagnetic induction to suspend and propel the train.

Slide 20:

Examples of electromagnetic induction
- Example 1: A coil with 200 turns and an area of 0.01 m² is exposed to a magnetic field changing at a rate of 0.02 T/s. Calculate the induced emf.
- Example 2: A conducting rod of length 0.5 m moves perpendicular to a magnetic field of 0.1 T at a speed of 2 m/s. Calculate the emf induced across the rod.
- Example 3: A transformer has a primary coil with 100 turns and a secondary coil with 500 turns. If the input voltage is 220 V, find the output voltage when the turns ratio is considered.
- Example 4: An alternating magnetic field with a frequency of 50 Hz passes through a coil with 100 turns. Calculate the rate of change of magnetic flux through the coil.
- Example 5: A wire with a length of 2 m is moved so that it cuts across a magnetic field at a rate of 0.05 T/s. If the wire carries a current of 0.5 A, calculate the induced emf.

Slide 21: Magnetic field due to a solenoid

A solenoid is a coil of wire wound tightly in the shape of a cylinder.
When a current passes through a solenoid, it creates a magnetic field inside the solenoid.
The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.
The formula to calculate the magnetic field inside a solenoid is given by B = μ₀nI, where B is the magnetic field strength, μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current running through the solenoid.
The direction of the magnetic field is determined by the right-hand rule.

Slide 22: Magnetic field due to a long straight wire

The magnetic field produced by a long straight wire follows a circular path around the wire.
The strength of the magnetic field decreases with increasing distance from the wire.
The formula to calculate the magnetic field B at a distance r from a long straight wire is given by B = (μ₀I)/(2πr), where μ₀ is the permeability of free space and I is the current in the wire.
The direction of the magnetic field is determined by the right-hand rule (thumb points in the direction of the current, fingers curl in the direction of the magnetic field).

Slide 23: Magnetic field due to a magnetic dipole

A magnetic dipole is a magnet with two equal and opposite poles separated by a distance.
The magnetic field around a magnetic dipole can be visualized using magnetic field lines.
The field lines emerge from the North pole, curve around and enter the South pole.
The strength of the magnetic field at a point near a magnetic dipole is given by the equation B = (μ₀Msinθ)/(4πr²), where B is the magnetic field strength, μ₀ is the permeability of free space, M is the magnetic dipole moment, θ is the angle between the magnetic field and the line connecting the point to the dipole, and r is the distance between the point and the dipole.

Slide 24: Torque on a magnetic dipole in a magnetic field

A magnetic dipole placed in a magnetic field experiences a torque.
The torque experienced by a magnetic dipole is given by the equation τ = MBsinθ, where τ is the torque, M is the magnetic dipole moment, B is the magnetic field strength, and θ is the angle between the magnetic dipole moment and the magnetic field.
The torque tends to align the magnetic dipole with the magnetic field.
The direction of the torque is perpendicular to the plane formed by the magnetic dipole moment and the magnetic field.

Slide 25: Magnetic field due to a current loop

A current loop is a closed path formed by a wire carrying a current.
The magnetic field produced by a current loop depends on its shape and orientation.
The magnetic field at the center of a circular current loop is given by the equation B = (μ₀nI)/(2R), where B is the magnetic field strength, μ₀ is the permeability of free space, n is the number of turns per unit length, I is the current, and R is the radius of the loop.
The direction of the magnetic field is perpendicular to the plane of the loop, following the right-hand rule.

Slide 26: Force between a current loop and a magnetic field

A current loop placed in a magnetic field experiences a force.
The force experienced by a current loop in a magnetic field is given by the equation F = BILsinθ, where F is the force, B is the magnetic field strength, I is the current in the loop, L is the length of the loop, and θ is the angle between the magnetic field and a plane normal to the loop.
The force tends to move the current loop to a position where its plane becomes parallel to the magnetic field.

Slide 27: Applications of magnetic forces and torques

Magnetic forces and torques find applications in various devices and technologies.
Electric motors, generators, and transformers rely on the interaction between magnetic fields and current-carrying conductors.
Magnetic levitation systems use magnetic forces to levitate objects.
Magnetic resonance imaging (MRI) machines use magnetic fields and torques to create detailed images of the body.
Magnetic particle inspection is used for flaw detection in materials.

Slide 28: Self-induction and inductance

Self-induction is the phenomenon in which a changing current in a coil induces an electromotive force (emf) in the same coil.
The induced emf opposes the change in current causing it, following Lenz’s law.
The property of a coil to induce a self-emf due to the changing current is known as inductance.
Inductance is denoted by the symbol L and measured in henries (H).
The induced emf is given by the equation emf = -L(dI/dt), where emf is the electromotive force, L is the inductance, and (dI/dt) is the rate of change of current.

Slide 29: Mutual inductance and transformers

Mutual inductance is the phenomenon in which a changing current in one coil induces an electromotive force (emf) in a neighboring coil.
The two coils are called the primary and secondary coils.
The induced emf in the secondary coil is proportional to the rate of change of current in the primary coil.
Mutual inductance is denoted by the symbol M and measured in henries (H).
Transformers are devices that utilize mutual inductance to transfer electrical energy between the primary and secondary coils.
Transformers can step up or step down the voltage of an electrical system.

Slide 30: Faraday’s law of electromagnetic induction

Faraday’s law of electromagnetic induction states that a change in magnetic field through a loop of wire induces an electromotive force (emf) in the loop.
The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux through the loop.
The formula for calculating the induced emf is emf = -N(dΦ/dt), where emf is the electromotive force, N is the number of turns in the loop, and (dΦ/dt) is the rate of change of magnetic flux.
Faraday’s law forms the basis of many devices and technologies in our daily lives, including generators, motors, and transformers.