I'm not sure if it makes sense to distinguish between state functions and non-state functions outside the field of thermodynamics.johankep said:Homework Statement:: . a state function and exact differential?
Relevant Equations:: state functions
is the magnetic field B→. a state function and exact differential?
I argued that it's a state function, what do you guys think
Philip Koeck said:I'm not sure if it makes sense to distinguish between state functions and non-state functions outside the field of thermodynamics.
How did you argue that B is a state function.
However, E is an exact differential in electrostatics since it is the gradient of a scalar field.
B is not the gradient of a scalar field.
Sorry forget to say..my argument was that since B can be measured knowing its current value(state) only..then it's a state function but I'm not sure to be honest if my reasoning correctPhilip Koeck said:I'm not sure if it makes sense to distinguish between state functions and non-state functions outside the field of thermodynamics.
How did you argue that B is a state function.
However, E is an exact differential in electrostatics since it is the gradient of a scalar field.
B is not the gradient of a scalar field.
Now I see why you ask. In a thermodynamic context I guess it can be important whether B is a state function or not.johankep said:Thanks for the reply Philip
regarding your question, this is the context of B here
https://en.wikipedia.org/wiki/Magnetic_Thermodynamic_Systems
Philip Koeck said:Now I see why you ask. In a thermodynamic context I guess it can be important whether B is a state function or not.
I don't understand very much about this, I'm afraid, but I'm a bit surprised about the equations in the wikipedia article.
In the second equation p dV is not integrated, whereas the other 3 terms are. Probably just a typo.
What worries me more is the last term which contains both a ΔB and a dV in the integrand. Is that really correct? Do you have a derivation? Maybe it should say B rather than ΔB.
B is not an extensive quantity, so I wouldn't expect it to show up as a difference or differential in the fundamental equation.
Then the integration over V is also strange. Which V? V is one of the quantities that changes.
Yes, the magnetic field B→ is a state function. This means that its value only depends on the current state of the system, and not on how the system reached that state. In other words, the magnetic field B→ is independent of the path taken to reach a certain point in space.
A state function is a physical quantity that only depends on the current state of the system, and not on the path taken to reach that state. Examples of state functions include temperature, pressure, and energy.
An exact differential is a mathematical concept that describes the change in a state function as a result of a small change in its independent variables. In other words, it is a precise and accurate way to calculate the change in a state function.
The magnetic field B→ is related to the exact differential through the Maxwell's equations, specifically the equation for the curl of the magnetic field. This equation states that the curl of the magnetic field is equal to the rate of change of the electric field, which is an exact differential.
Knowing that the magnetic field B→ is a state function and can be described by an exact differential allows us to accurately and precisely calculate its behavior and changes in different situations. This is crucial in understanding and predicting the behavior of magnetic fields in various systems and applications, such as in electronics and electromagnetism.