Right Hand Thumb Rule: Maxwell's Conclusions

[sambarbarian]

how did maxwell arrive at the conclusion that the direction of magnetic field is the way our fingers curl , with thumb in direction of current ?

 

[mfb]

The definition of the direction of magnetic field lines is an arbitrary convention (like the technical current direction, too). You could use the left hand and say "ok, magnetic field lines go from south to north". You would have to modify the sign in some equations, but it would work.

 

[DragonPetter]

how did maxwell arrive at the conclusion that the direction of magnetic field is the way our fingers curl , with thumb in direction of current ?

Its a consequence of the vector mathematics. The right hand thumb rule is just a learning tool to describe that part of the mathematics. I doubt Maxwell was holding his right hand out while trying to understand things, although its possible if he learned vector calculus that way (although he helped develop the math as we know it today).

 

[sambarbarian]

so , we cannot be sure which direction the field is taking ?

 

[mikeph]

It is a matter of definitions, not physics. In particular, it is the result of using a right-handed coordinate system, where (1,0,0)x(0,1,0)=(0,0,1), the three vectors pointing, respectively, in the direction of a human's index finger,middle finger,and thumb.

As with any coordinate system, the choice does not affect reality, but it does affect our own calculations .

 

[Khashishi]

If the magnetic field is pointing north, that doesn't mean that there is actually some real substance that is moving or facing north (and not south). The magnetic field is actually just one way of representing three components of the electromagnetic tensor. Indeed, the x component of the magnetic field is associated with the y-z or z-y component of the electromagnetic tensor, because it is associated with current in the y-z or z-y plane. It doesn't really have anything to do with the x direction. x is just a convenient label because in 3 dimensions, x is "dual" to yz and y is "dual" to xz and z is "dual" to xy. What this means is there's a 1 to 1 correspondence between vectors in x,y,z space and area elements in xy, xz, yz space.

The cross product is really just a shorthand for this dual space relationship. A similar relationship exists for angular momentum. (Angular momentum in the z direction actually has nothing to do with z; it is motion in the x-y directions). If you want to extend the theory to higher than 3 dimensions, you need to take this into account.