# Work/Energy in a Magnetic Field

• MyoPhilosopher
In summary, the conversation discusses the concept of work and energy in relation to magnetic forces. It is mentioned that the force is responsible for the change in momentum but not the change in rotational kinetic energy. This is similar to the friction between a car's wheels and the road. The conversation also debates the term "magnetic potential energy" and whether it accurately reflects the forces at play.
MyoPhilosopher
Homework Statement
A compass needle has a magnetic moment of 𝜇. At its location, the magnitude of the Earth’s magnetic field is 𝑩 northward at 𝜃 below the horizontal. Identify the orientations of the needle that represent (a) the minimum potential energy and (b) the maximum potential energy of the needle–field system. (c) How much work must be done on the system to move the needle from the minimum to the maximum potential energy orientation?
Relevant Equations
ΔU = -μBcos(θ)
Sorry if I am asking in the wrong fashion as I am new.

The above questions are easily solvable:
1) U = -μBcos(0)
2) U = -μBcos(180)
3) W = ΔU = 2) - 1)

My question is more related to some theory: where is this work/energy coming from since a magnetic force, to my knowledge can't do "work"?
What force is doing -W (minus W), is it simply the magnetic field, or is there another concrete equation to demonstrate what exactly is happening.

Thank you for anyone that can explain or possibly ask me directional questions

Delta2
It's one of those bizarre situations in physics where a force is responsible for the change in momentum (angular momentum in this case since the needle rotates) but is not responsible for the change in the (rotational) kinetic energy (of the needle). For the latter are responsible internal electrostatic forces that appear inside the needle.
Another example of such a force is the friction between a car's wheels and the road. We all know that a car cannot move without friction, however we all also know that the work isn't done by friction but by the car's engine. So friction is responsible for the change in the momentum of the car, but internal forces at car's engine are responsible for the work done that increases the kinetic energy of the car.

Last edited:
MyoPhilosopher
Delta2 said:
It's one of those bizarre situations in physics where a force is responsible for the change in momentum (angular momentum in this case since the needle rotates) but is not responsible for the change in the (rotational) kinetic energy (of the needle). For the latter are responsible internal electrostatic forces that appear inside the needle.
Another example of such a force is the friction between a car's wheels and the road. We all know that a car cannot move without friction, however we all also know that the work isn't done by friction but by the car's engine. So friction is responsible for the change in the momentum of the car, but internal forces at car's engine are responsible for the work done that increases the kinetic energy of the car.

Thank you for taking the time, great answer!

berkeman
Delta2 said:
It's one of those bizarre situations in physics where a force is responsible for the change in momentum (angular momentum in this case since the needle rotates) but is not responsible for the change in the (rotational) kinetic energy (of the needle). For the latter are responsible internal electrostatic forces that appear inside the needle.
Another example of such a force is the friction between a car's wheels and the road. We all know that a car cannot move without friction, however we all also know that the work isn't done by friction but by the car's engine. So friction is responsible for the change in the momentum of the car, but internal forces at car's engine are responsible for the work done that increases the kinetic energy of the car.

So it really shouldn't be referred to as "magnetic potential energy" then, right?

The change in the potential energy should be the work done by the magnetic force, but the magnetic force can do no work. I guess it is just a shorthand way of referring to the potential energy associated with a magnetic dipole in a magnetic field. Saying the electric potential energy in this case, would just confuse people.

Rolls With Slipping said:

So it really shouldn't be referred to as "magnetic potential energy" then, right?

The change in the potential energy should be the work done by the magnetic force, but the magnetic force can do no work. I guess it is just a shorthand way of referring to the potential energy associated with a magnetic dipole in a magnetic field. Saying the electric potential energy in this case, would just confuse people.
Well yes the magnetic field can't do work on matter, hence the term magnetic potential energy becomes problematic at first glance. However we can attribute the work of the internal electric forces as (pseudo) work of the magnetic field force and this can make the magnetic potential energy term viable again.

## What is work/energy in a magnetic field?

Work/energy in a magnetic field is the concept of how a magnetic field can affect the movement and energy of an object. It involves the interaction between a magnetic field and a charged particle, resulting in a change in the particle's kinetic energy.

## How is work/energy calculated in a magnetic field?

Work/energy in a magnetic field can be calculated using the formula W=qVBsinθ, where W is the work done, q is the charge of the particle, B is the strength of the magnetic field, V is the velocity of the particle, and θ is the angle between the particle's velocity and the magnetic field.

## What is the relationship between magnetic fields and work/energy?

Magnetic fields can do work on charged particles by exerting a force on them. This force can change the direction and speed of the particle, resulting in a change in its kinetic energy. This work done by the magnetic field is equal to the change in the particle's kinetic energy.

## Does the direction of the magnetic field affect work/energy?

Yes, the direction of the magnetic field can affect the work/energy of a charged particle. The work done by a magnetic field is dependent on the angle between the particle's velocity and the magnetic field. If the angle is 90 degrees, no work is done. If the angle is less than 90 degrees, work is done in the direction of the particle's motion. If the angle is greater than 90 degrees, work is done opposite to the particle's motion.

## Can work be done by a magnetic field on a stationary particle?

No, work cannot be done by a magnetic field on a stationary particle. For work to be done, there must be a change in kinetic energy, which requires the particle to have a velocity. A stationary particle does not have a velocity, so no work can be done on it by a magnetic field.

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