Is Biot-Savart's Law Consistent with Early Physics Principles?

[vishureddy]

Why Biot and Savarat assumed that magnetic field due to a current carrying wire is proportional to current ?

How did they measure the current in those days when even ohms law was not discovered?

If they have used an instrument like an ammeter there is a problem with it .An ammeter works on an assumption that the deflection of the coil in it is proportional to current which in turn is proportional to magnetic field .How can we use this assumption to define the magnetic field around a wire?

What are the first definitions given to magnetic field and current?

And my last doubt is
is biot savarats law consistent with laws in laws in physics that are established before it?


thanks a lot in advance for clarifying the doubts

 

[Naty1]

Can't answer the history aspects...but try here and see if Amperes and Gausses laws were instrumental...

http://en.wikipedia.org/wiki/Biot-Savart_law

Maybe the relationships were measured experimentally rather than based on some esoteric theory, but I really don't know...Often people who did lots of early experiments had intuitive insights from experience and tested them and gradually formed a "law" that we take for granted today...

 

[shakgoku]

To prove that magnetic field is proportional to current associated with the wire, we have to measure the magnetic field and current. At that time it was tricky. They defined unit of current in terms of magnetic force between 2 straight wires.(ampere). Magnetic field can be measured by placing a compass near current carrying wire and moving it towards and away and noting its deflection from magnetic field lines of earth.so if we take Earth's field is 1 unit, then we measure field strength of wire relative to it.
Note:(from griffiths electrodynamics)
Permeability of free space serves to define an ampere and ampere in turn defines coulomb.

 

[Born2bwire]

I think you may be going about this backwards. The electric and magnetic fields are force fields. They are used to describe the forces between sources, charges and currents. This is no different than with gravitational fields. When we have two masses in proximity then they experience a force due to each other. Now we can describe this force purely as a relationship between the two (F = G*m1*m2/r^2) or we can say that one mass creates a gravity field (Grav_Field = G*m1/r^2) and this field causes a force on any mass in its presence, where F = Grav_Field*m.

This is of course a trivial example but it is no different than the electric field between two charges.

So static charges experience a force that we can describe by a field we call the electric field. Currents experience a force that we can describe by a field we call the magnetic field.

So the magnetic field is produced by and is proportional to currents simply by definition. I think it is probably more accurate to say that the force between two currents was observed and out of this came the magnetic field as opposed to the opposite. It would then be a question of empirical observation and experimentation to determine how to describe the magnetic force (and its field) in terms of current, position, direction, etc. But once these rules were established (or at least the proportionality of the force with respect to current) then the ammeter would naturally come about.

 

[pmacias]

I would like to address the concerns regarding Biot-Savart's law and its assumptions.

Firstly, it is important to understand that Biot-Savart's law is an empirical law, which means it is based on observations and experiments rather than theoretical reasoning. Therefore, the assumption that the magnetic field due to a current-carrying wire is proportional to the current is based on experimental evidence.

The measurement of current in the time of Biot and Savart was indeed a challenge. They used instruments like the tangent galvanometer, which measures the horizontal component of the magnetic field produced by a current-carrying wire. However, it is worth noting that even with modern instruments, the measurement of current is not a straightforward process and requires calibration and verification.

Regarding the use of an ammeter, it is true that it works on the assumption that the deflection of the coil is proportional to the current. However, this assumption can be verified and calibrated using known currents and comparing the readings. Therefore, it is a reliable method for measuring current.

The first definitions of magnetic field and current were given by scientists such as Hans Christian Oersted and Andre-Marie Ampere. Oersted defined the magnetic field as the force acting on a magnetic needle placed near a current-carrying wire, while Ampere defined current as the flow of electric charge. These definitions are still used today, and Biot-Savart's law is consistent with them.

In conclusion, while there may be some limitations and assumptions in Biot-Savart's law, it has been extensively tested and found to be consistent with other established laws in physics. As with any scientific theory, it is subject to further experimentation and refinement, but for now, it remains a valuable tool for understanding and predicting magnetic fields.