# Magnetic field does no work -- true in all branches of physics?

• CPW
In summary, the conversation discusses the force on a charged particle moving through a magnetic field and how it cannot change the particle's kinetic energy because the force is always perpendicular to the velocity. The individual also mentions that this fact is stated in introductory physics textbooks and is applicable to all branches of physics, including high energy physics and particle beam accelerators. They also mention the use of magnetic fields to steer particle beams and ask for clarification on whether magnetic fields do work in all situations. Another individual adds that a current loop or magnetic moment in a magnetic field can experience a torque that can increase kinetic energy.
CPW
The force on a charged particle that is moving through a magnetic field is explained in introductory physics textbooks. The magnetic field cannot change the kinetic energy of the charged particle because the force from the magnetic field is always perpendicular to the velocity, so no work is done.

My question: Is that fact true in all branches of physics, such as high energy physics?

Synchrotron radiation might be of your interest though I am not qualified to explain it.

anuttarasammyak said:
Synchrotron radiation might be of your interest though I am not qualified to explain it.

Hi. Thank you for the recommendation.

I studied particle beam accelerators, and those textbooks also state only the electric fields can be used to change the kinetic energy of the charged particle being accelerated. The magnetic fields do no work, even in situations when the charged particle's speed is relativistic. (The magnetic fields are used to steer the particle beam).

So, my thought is that magnetic fields do no work in all branches of physics. Even esoteric realms of which I am ignorant.

It might interest the OP that a current loop and/or a magnetic moment in a magnetic field experiences a torque which can result in an increase in kinetic energy.

CPW

## 1. How can a magnetic field do no work?

A magnetic field does not do work because it is a conservative force. This means that the work done by a magnetic field on a charged particle depends only on the initial and final positions of the particle, and not on the path taken. Therefore, the work done by a magnetic field on a charged particle in a closed loop is zero.

## 2. Is this true in all branches of physics?

Yes, the concept of a magnetic field doing no work is true in all branches of physics. This is because the laws of electromagnetism, which govern the behavior of magnetic fields, are fundamental and apply to all physical systems.

## 3. How does this relate to the conservation of energy?

The fact that a magnetic field does no work is related to the conservation of energy. Since the work done by a magnetic field is zero, the energy of a charged particle in a magnetic field is conserved. This means that the total energy of the particle remains constant, and no energy is lost or gained due to the presence of the magnetic field.

## 4. Can a magnetic field ever do work?

While a magnetic field does no work on a charged particle in a closed loop, it can do work on a charged particle that is moving in a non-closed path. This is because the work done by a magnetic field on a charged particle depends on the angle between the magnetic field and the velocity of the particle. If the particle is moving at an angle to the magnetic field, work is done and the particle's energy changes.

## 5. How does this concept apply to everyday life?

The concept of a magnetic field doing no work has many practical applications in everyday life. For example, it is the principle behind the operation of electric motors and generators, which use magnetic fields to convert electrical energy into mechanical energy and vice versa. It also explains why magnets can hold objects in place without expending any energy, as the magnetic field does no work on the objects.

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