Potential energy and torque in a magnetic field

In summary, when a coil's magnetic dipole moment is perpendicular to a uniform magnetic field, μ × B indicates maximum torque due to sin90 being equal to 1. However, -μ dot B reflects zero potential energy since cos90 is equal to 0. This may seem contradictory, but when the coil is rotated to a perpendicular angle and released, it will automatically rotate until the angle is 0. This is because the zero of potential energy is not its minimum and the torque is trying to align the dipole moment to this minimum energy configuration. This clarifies the idea that even though there is no potential energy, the torque still exists and can cause the coil to rotate.
  • #1
BrianC12
18
0
If you have a coil with its magnetic dipole moment perpendicular to a uniform magnetic field, μ × B says that there will be maximum torque since sin90 is 1. But at the same time, -μ dot B gives the potential energy and cos90 is 0. What I don't understand is how you can have torque at this angle, but no potential energy. If you rotate the coil to a perpendicular angle and release it, it'll automatically rotate until the angle is 0. If there were no potential energy wouldn't it just stay in that position?
 
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  • #2
The zero of potential energy here is not its minimum. When the magnetic field and dipole moment are aligned, you get [itex]-\mu \cdot B = -|\mu||B|[/itex]. The torque is trying to align the dipole moment to this minimum energy configuration.
 
  • #3
Ahh alright that makes sense, thanks.
 

1. What is potential energy in a magnetic field?

Potential energy in a magnetic field refers to the energy stored in a system due to the interaction between a magnetic field and an object with magnetic properties, such as a magnet or a charged particle. This energy can be converted into other forms, such as kinetic energy, when the magnetic field or the object is moved or changed.

2. How is potential energy related to torque in a magnetic field?

Potential energy and torque are closely related in a magnetic field. Torque is a measure of the rotational force acting on an object, while potential energy is a measure of the stored energy in a system. In a magnetic field, the torque acting on an object with magnetic properties is directly proportional to the change in potential energy of the object.

3. What factors affect the potential energy in a magnetic field?

The potential energy in a magnetic field is affected by several factors, including the strength of the magnetic field, the orientation of the magnetic field, the distance between the object and the magnetic field, and the magnetic properties of the object (e.g. its magnetic moment).

4. Can potential energy be negative in a magnetic field?

Yes, potential energy can be negative in a magnetic field. This occurs when the orientation of the object's magnetic moment is opposite to that of the magnetic field, resulting in a negative torque and a decrease in potential energy. This is similar to how potential energy can be negative in a gravitational field when an object is moving in the opposite direction of the gravitational force.

5. How is potential energy and torque in a magnetic field used in real-world applications?

Potential energy and torque in a magnetic field have many practical applications, such as in electric motors, generators, and magnetic levitation systems. These phenomena are also essential in understanding the behavior of particles in magnetic fields, such as in particle accelerators and fusion reactors.

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