# Angular momentum of a solenoid

• dishku
In summary, a solenoid with radius R, n turns per unit length, and carrying current I, has two long cylinder shells coaxial to it - one inside at radius a and carrying a charge +Q, and one outside at radius b and carrying a charge -Q. When the current in the solenoid is gradually reduced, the magnetic field changes and provides a Lorentz force which accelerates the charge particles in the cylinders. This leads to the rotation of the cylinders and the generation of angular momentum. The direction of the Lorentz force is determined by the right hand first rule, which states that the current direction is perpendicular to the direction of the magnetic field. However, the exact mechanism and geometry of the Lorent

#### dishku

imagine a very long solenoid with radius R ,n turn per unit length , carry current I.coaxial with the solenoid are two long cylinder shell of length L-one ,inside the solenoid at radius a ,carries a charge +Q,uniform distributed over its surface;the other ,outside the solenoid at radius b,carries charge -Q. when the current in the solenoid is gradually reduce , the cylinder begin to rotate.
WHERE DOES THE ANGULAR MOMENTUM COME FROM ?

when current gradually reduce,the magnetic field changes,provides lorentz force(biot savrat rule),it accelerates charge particle,since cylinders are base for those particles feel force of the lorentz,thats the way angular momentum comes from ,
i have not tried to look geometrically,

Initially there are no currents. So there is no Lorentz force. There is a radial electric field between the two charged cylinders, and an axial magnetic field in the solenoid. When the magnetic field is reduced, the dB/dt induces a tangential eddy current in the inner cylinder, if it is a conductor. There will be a radial force (Lorentz I x B force) on the inner cylinder if it is a conductor, but no tangential force. The Lorentz force, because it is perpendicular to the current direction, can not "accelerate" it.

i am a high school student and lack many terminologies,i also don't know whether the charge particles at rest acted by changing magnetic field will feel force and if it feels in what direction
here, when current is flowing through cylinder, the magnetic field is parellel to tangent on the surface of cylinder, and we we can clearly that the changing magnetic flux is traveling from one end of cylinder to other end

now according to my book by right hand first rule , when magnetic field travels in thumb directin current should flow in in the direction in which other finger curls, since charge particles Q and -Q are also medias of current , they need to flow as per the right hand first rule which makes cylinder rotate and i don't what the force is called, lorentz or other because charge particle in rest or may be its lorentz force considered due to changing magnetic field which enhances relative motion between charge particle and magnetic flux(thus relative velocity) .
what ever because since i am high school student i don't know exact mechanism of geometry of lorentz force direction but i know that that tthe force comes due to the interaction of magnetic field of charge particles and acting magnetic field, this is how i understood
if u have any commentpls reply bob s

## 1. What is the definition of angular momentum of a solenoid?

The angular momentum of a solenoid is a measure of the rotational motion of the solenoid around an axis. It is a vector quantity that depends on the mass, velocity, and distance from the axis of rotation.

## 2. How is the angular momentum of a solenoid calculated?

The angular momentum of a solenoid can be calculated by multiplying the moment of inertia of the solenoid by its angular velocity. The moment of inertia is a measure of the distribution of mass around the axis of rotation.

## 3. What factors affect the angular momentum of a solenoid?

The angular momentum of a solenoid is affected by its moment of inertia, angular velocity, and the radius of the solenoid. Additionally, external forces such as friction or torque can also affect the angular momentum.

## 4. How is the angular momentum of a solenoid conserved?

According to the law of conservation of angular momentum, the total angular momentum of a closed system remains constant. Therefore, any changes in the angular momentum of a solenoid must be counteracted by changes in the angular momentum of other objects within the system.

## 5. What are the applications of angular momentum of a solenoid?

The angular momentum of a solenoid has various applications in physics and engineering, such as in the design of motors and generators. It is also used in fields like gyroscopy, where the angular momentum of a spinning solenoid is used to measure changes in orientation.