There is some confusion or misinformation about the magnetic field, represented by the B-vector and force. So I inquired to chatGPT which gave the commonly accepted scientific explanation. I encourage all to look it up for themselves or confirm by experiment.
Regards,
bi
B-field vs Force
ChatGPT
bi
Talking about a magnetic field produced by a permanent magnet or solenoid electromagnet with a ferromagnetic core, it is referred to as a B-field represented by a B-vector at each point in the affected space, that B-vector having a direction and magnitude (in Tesla or Webers/m^2). Is this B-vector a force vector like a physical force in newtons caused by something like gravity or impact?
ChatGPT
No, the B-vector, or magnetic flux density, is not a force vector like a physical force measured in newtons. Instead, it represents the strength and direction of the magnetic field at each point in space. The B-field is measured in teslas (T) or webers per square meter (Wb/m²).
While the B-field itself is not a force, it does interact with moving electric charges and magnetic dipoles, such as current-carrying conductors or magnetic moments, to produce forces. The force
F experienced by a moving charge
q in a magnetic field
B is given by the Lorentz force law:
F=q(v×B)
where
v is the velocity of the charge and
×
× denotes the cross product.
Similarly, a current-carrying wire in a magnetic field experiences a force given by:
F=I(L×B)
where
I is the current and
L is a vector representing the length and direction of the wire.
In both cases, the magnetic field
B interacts with the charge or current to produce a force, but the
B-vector itself is not a force vector.
bi
Thanks. Please explain how force develops from the interaction between two magnets, like poles (repulsion), and unlike poles (attraction), and between a magnet and a ferromagnetic object, relating to the B-field(s).
ChatGPT
The force between two magnets or between a magnet and a ferromagnetic object arises due to the interaction of their magnetic fields. Here's how these forces develop, relating to the B-fields:
Interaction Between Two Magnets
Like Poles (Repulsion)
When the like poles (e.g., north-north or south-south) of two magnets are brought close to each other, their B-fields interact in a way that causes repulsion. Here's why:
Field Lines and Direction: The magnetic field lines of both magnets point away from their north poles and toward their south poles. When two north poles are close to each other, the field lines repel each other because they are in the same direction and do not combine smoothly.
Energy Minimization: The magnetic system seeks to minimize energy, and repulsion occurs because it would require work to bring the like poles closer against the repulsive force of their aligned field lines.
Force Calculation: The force between the two magnets can be calculated using the concept of the magnetic dipole moment. The magnetic force between two magnetic dipoles (m1 and m2) separated by a distance r is:
F∝(3(1⋅)(2⋅)−1⋅2)/r^5
Unlike Poles (Attraction)
When the unlike poles (e.g., north-south) of two magnets are brought close to each other, they attract. Here's why:
Field Lines and Direction: The field lines from the north pole of one magnet naturally extend to the south pole of the other magnet, creating a smooth, continuous field line flow between the poles. This lowers the system's potential energy.
Energy Minimization: The system seeks to minimize energy, and attraction occurs because the unlike poles align their field lines, thus reducing the magnetic potential energy.
Force Calculation: The attractive force can also be understood through the dipole interaction as described above, where the interaction between opposite dipoles leads to attraction.
Interaction Between a Magnet and a Ferromagnetic Object
Magnetization of the Object: When a ferromagnetic object (like iron) is placed in the B-field of a magnet, the magnetic domains within the ferromagnetic material align with the external B-field. This induced magnetization effectively turns the object into a temporary magnet with its own north and south poles.
Attraction Mechanism: The magnet and the induced poles of the ferromagnetic object interact. The induced south pole of the object is attracted to the north pole of the magnet, and vice versa, resulting in an attractive force.
Force Calculation: The force can be estimated using:
F=∇(m⋅B)
Here,
m is the magnetic moment of the induced dipole in the ferromagnetic material, and
B is the magnetic field of the permanent magnet. The force is the gradient of the potential energy of the magnetic dipole in the external B-field.
In summary, the magnetic B-field interactions give rise to forces due to the alignment of magnetic moments and the tendency of the system to minimize energy by either attracting unlike poles or repelling like poles. These forces can be calculated using principles from the magnetic dipole moment interactions and the behavior of magnetic fields in space.
Thanks. bi
ChatGPT
Memory updated
You're welcome! If you have any more questions or need further clarification, feel free to ask
ChatGPT
bi
Talking about a magnetic field produced by a permanent magnet or solenoid electromagnet with a ferromagnetic core, it is referred to as a B-field represented by a B-vector at each point in the affected space, that B-vector having a direction and magnitude (in Tesla or Webers/m^2). Is this B-vector a force vector like a physical force in newtons caused by something like gravity or impact?
ChatGPT
No, the B-vector, or magnetic flux density, is not a force vector like a physical force measured in newtons. Instead, it represents the strength and direction of the magnetic field at each point in space. The B-field is measured in teslas (T) or webers per square meter (Wb/m²).
While the B-field itself is not a force, it does interact with moving electric charges and magnetic dipoles, such as current-carrying conductors or magnetic moments, to produce forces. The force
F experienced by a moving charge
q in a magnetic field
B is given by the Lorentz force law:
F=q(v×B)
where
v is the velocity of the charge and
×
× denotes the cross product.
Similarly, a current-carrying wire in a magnetic field experiences a force given by:
F=I(L×B)
where
I is the current and
L is a vector representing the length and direction of the wire.
In both cases, the magnetic field
B interacts with the charge or current to produce a force, but the
B-vector itself is not a force vector.
bi
Thanks. Please explain how force develops from the interaction between two magnets, like poles (repulsion), and unlike poles (attraction), and between a magnet and a ferromagnetic object, relating to the B-field(s).
ChatGPT
The force between two magnets or between a magnet and a ferromagnetic object arises due to the interaction of their magnetic fields. Here's how these forces develop, relating to the B-fields:
Interaction Between Two Magnets
Like Poles (Repulsion)
When the like poles (e.g., north-north or south-south) of two magnets are brought close to each other, their B-fields interact in a way that causes repulsion. Here's why:
Field Lines and Direction: The magnetic field lines of both magnets point away from their north poles and toward their south poles. When two north poles are close to each other, the field lines repel each other because they are in the same direction and do not combine smoothly.
Energy Minimization: The magnetic system seeks to minimize energy, and repulsion occurs because it would require work to bring the like poles closer against the repulsive force of their aligned field lines.
Force Calculation: The force between the two magnets can be calculated using the concept of the magnetic dipole moment. The magnetic force between two magnetic dipoles (m1 and m2) separated by a distance r is:
F∝(3(1⋅)(2⋅)−1⋅2)/r^5
Unlike Poles (Attraction)
When the unlike poles (e.g., north-south) of two magnets are brought close to each other, they attract. Here's why:
Field Lines and Direction: The field lines from the north pole of one magnet naturally extend to the south pole of the other magnet, creating a smooth, continuous field line flow between the poles. This lowers the system's potential energy.
Energy Minimization: The system seeks to minimize energy, and attraction occurs because the unlike poles align their field lines, thus reducing the magnetic potential energy.
Force Calculation: The attractive force can also be understood through the dipole interaction as described above, where the interaction between opposite dipoles leads to attraction.
Interaction Between a Magnet and a Ferromagnetic Object
Magnetization of the Object: When a ferromagnetic object (like iron) is placed in the B-field of a magnet, the magnetic domains within the ferromagnetic material align with the external B-field. This induced magnetization effectively turns the object into a temporary magnet with its own north and south poles.
Attraction Mechanism: The magnet and the induced poles of the ferromagnetic object interact. The induced south pole of the object is attracted to the north pole of the magnet, and vice versa, resulting in an attractive force.
Force Calculation: The force can be estimated using:
F=∇(m⋅B)
Here,
m is the magnetic moment of the induced dipole in the ferromagnetic material, and
B is the magnetic field of the permanent magnet. The force is the gradient of the potential energy of the magnetic dipole in the external B-field.
In summary, the magnetic B-field interactions give rise to forces due to the alignment of magnetic moments and the tendency of the system to minimize energy by either attracting unlike poles or repelling like poles. These forces can be calculated using principles from the magnetic dipole moment interactions and the behavior of magnetic fields in space.
Thanks. bi
ChatGPT
Memory updated
You're welcome! If you have any more questions or need further clarification, feel free to ask
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