What is Fleming's left hand rule and Lorentz force?
1 Answer
### Fleming's Left-Hand Rule
Fleming's Left-Hand Rule is a guideline used in electromagnetism to determine the direction of motion of a conductor (or wire) that carries current and is placed in a magnetic field. It applies specifically to electric motors.
Fleming's Left-Hand Rule states that if you stretch the **thumb**, **index finger**, and **middle finger** of your left hand at right angles to each other (forming a 90° angle), each finger represents a different physical quantity:
- **Thumb**: Direction of the **force** (motion) acting on the conductor.
- **Index finger**: Direction of the **magnetic field** (from north to south).
- **Middle finger**: Direction of the **current** (flow of electrons) in the conductor.
In simpler terms, if you know the direction of the magnetic field and the direction of the current, you can use this rule to find the direction in which the conductor will move (the force on the conductor).
#### Example:
If a current-carrying wire is placed in a magnetic field, the direction of the force that acts on the wire can be found using Fleming's Left-Hand Rule:
1. Point your **index finger** in the direction of the magnetic field (from north to south).
2. Point your **middle finger** in the direction of the current (flow of electrons).
3. Your **thumb** will point in the direction of the force, which is the direction the wire will move.
Fleming's Left-Hand Rule is crucial for understanding how electric motors work. The electric motor operates by creating a magnetic field around a coil of wire carrying a current. The interaction of this magnetic field with the external magnetic field generates a force that makes the coil rotate, producing mechanical work.
### Lorentz Force
The Lorentz force is the total force experienced by a charged particle moving in an electromagnetic field. This force is a combination of two fundamental forces:
1. The **electric force** acting on the charged particle.
2. The **magnetic force** acting on the charged particle.
The Lorentz force law can be written as:
\[
\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})
\]
Where:
- \( \mathbf{F} \) is the total force on the charged particle.
- \( q \) is the charge of the particle.
- \( \mathbf{E} \) is the electric field acting on the particle.
- \( \mathbf{v} \) is the velocity of the particle.
- \( \mathbf{B} \) is the magnetic field.
- \( \mathbf{v} \times \mathbf{B} \) represents the **cross product** of the velocity vector and the magnetic field vector, which gives the direction of the magnetic force.
#### Key points about the Lorentz Force:
- **Electric Force**: The electric field \( \mathbf{E} \) exerts a force on a charged particle based on its charge \( q \). The direction of the force is the same as the direction of the electric field for positive charges and opposite for negative charges.
- **Magnetic Force**: The magnetic force is more complex. The force on a moving charged particle depends on the velocity of the particle \( \mathbf{v} \) and the magnetic field \( \mathbf{B} \). The direction of the magnetic force is given by the **right-hand rule** for the cross product \( \mathbf{v} \times \mathbf{B} \). This force is perpendicular to both the velocity of the particle and the magnetic field.
#### Example of Lorentz Force:
Consider a positively charged particle moving through a uniform magnetic field:
1. The **electric force** would push the particle along the direction of the electric field.
2. The **magnetic force** would push the particle in a direction perpendicular to both the velocity of the particle and the magnetic field, causing it to follow a curved path (typically circular or helical, depending on the presence of electric fields).
### Relation between Fleming's Left-Hand Rule and Lorentz Force
Both Fleming's Left-Hand Rule and the Lorentz force are related to the interaction between current (moving charges) and magnetic fields:
- Fleming's Left-Hand Rule is specifically applied in the context of a **current-carrying conductor** in a magnetic field. It helps us predict the motion of the conductor (e.g., the force that causes a motor to rotate).
- The Lorentz force, on the other hand, applies to **individual charged particles** in both electric and magnetic fields. It's a more general principle that describes how a charged particle moves under the influence of these fields.
In both cases, the force is a result of the interaction between the **magnetic field** and **moving charges**, and they both depend on the direction and magnitude of the charge's velocity, the magnetic field, and sometimes the electric field.
Fleming's Left-Hand Rule is a guideline used in electromagnetism to determine the direction of motion of a conductor (or wire) that carries current and is placed in a magnetic field. It applies specifically to electric motors.
Fleming's Left-Hand Rule states that if you stretch the **thumb**, **index finger**, and **middle finger** of your left hand at right angles to each other (forming a 90° angle), each finger represents a different physical quantity:
- **Thumb**: Direction of the **force** (motion) acting on the conductor.
- **Index finger**: Direction of the **magnetic field** (from north to south).
- **Middle finger**: Direction of the **current** (flow of electrons) in the conductor.
In simpler terms, if you know the direction of the magnetic field and the direction of the current, you can use this rule to find the direction in which the conductor will move (the force on the conductor).
#### Example:
If a current-carrying wire is placed in a magnetic field, the direction of the force that acts on the wire can be found using Fleming's Left-Hand Rule:
1. Point your **index finger** in the direction of the magnetic field (from north to south).
2. Point your **middle finger** in the direction of the current (flow of electrons).
3. Your **thumb** will point in the direction of the force, which is the direction the wire will move.
Fleming's Left-Hand Rule is crucial for understanding how electric motors work. The electric motor operates by creating a magnetic field around a coil of wire carrying a current. The interaction of this magnetic field with the external magnetic field generates a force that makes the coil rotate, producing mechanical work.
### Lorentz Force
The Lorentz force is the total force experienced by a charged particle moving in an electromagnetic field. This force is a combination of two fundamental forces:
1. The **electric force** acting on the charged particle.
2. The **magnetic force** acting on the charged particle.
The Lorentz force law can be written as:
\[
\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})
\]
Where:
- \( \mathbf{F} \) is the total force on the charged particle.
- \( q \) is the charge of the particle.
- \( \mathbf{E} \) is the electric field acting on the particle.
- \( \mathbf{v} \) is the velocity of the particle.
- \( \mathbf{B} \) is the magnetic field.
- \( \mathbf{v} \times \mathbf{B} \) represents the **cross product** of the velocity vector and the magnetic field vector, which gives the direction of the magnetic force.
#### Key points about the Lorentz Force:
- **Electric Force**: The electric field \( \mathbf{E} \) exerts a force on a charged particle based on its charge \( q \). The direction of the force is the same as the direction of the electric field for positive charges and opposite for negative charges.
- **Magnetic Force**: The magnetic force is more complex. The force on a moving charged particle depends on the velocity of the particle \( \mathbf{v} \) and the magnetic field \( \mathbf{B} \). The direction of the magnetic force is given by the **right-hand rule** for the cross product \( \mathbf{v} \times \mathbf{B} \). This force is perpendicular to both the velocity of the particle and the magnetic field.
#### Example of Lorentz Force:
Consider a positively charged particle moving through a uniform magnetic field:
1. The **electric force** would push the particle along the direction of the electric field.
2. The **magnetic force** would push the particle in a direction perpendicular to both the velocity of the particle and the magnetic field, causing it to follow a curved path (typically circular or helical, depending on the presence of electric fields).
### Relation between Fleming's Left-Hand Rule and Lorentz Force
Both Fleming's Left-Hand Rule and the Lorentz force are related to the interaction between current (moving charges) and magnetic fields:
- Fleming's Left-Hand Rule is specifically applied in the context of a **current-carrying conductor** in a magnetic field. It helps us predict the motion of the conductor (e.g., the force that causes a motor to rotate).
- The Lorentz force, on the other hand, applies to **individual charged particles** in both electric and magnetic fields. It's a more general principle that describes how a charged particle moves under the influence of these fields.
In both cases, the force is a result of the interaction between the **magnetic field** and **moving charges**, and they both depend on the direction and magnitude of the charge's velocity, the magnetic field, and sometimes the electric field.