Point of application of magnetic torque.

[anmol21]

Homework Statement

Hello,
When a current carrying loop (of any shape) is placed in a uniform magnetic field B , the field is given by MχB where M is the magnetic moment vector I*A where I Is current and A is the area vector. I want to know at which point or for which axis is the torque applied given by the above equation.

Homework Equations

ζ=MχB
M=I*A

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi anmol21! welcome to pf!

if B is uniform, the resultant force will be zero, so the effect is a pure torque

so the circuit will turn about the centre of mass of whatever the circuit is fixed to (or about whatever axis that is constrained to turn around)

 

[anmol21]

Thanks tiny-tim :)

So is the magnetic torque independent of the axis chosen ?

For example , Consider a sphere with a ring attached to it , with current I in the ring , in rotational equilibrium on a rough inclined plane. The magnetic field is vertically downwards and gravity is present. So we can equate the torque due to gravity and the magnetic torque at any point . So will be the magnetic torque be same even at the point of contact of the sphere with the ground or the centre of the sphere ?

 

[tiny-tim]

hi anmol21!

the magnetic torque of a uniform magnetic field on a circuit is a couple …

it is exactly the same as a couple (or "pure moment") in mechanics: it has the same moment about any point

"a system of forces with a resultant (a.k.a. net, or sum) moment but no resultant force"

"… the moment (torque) of a couple is independent of the reference point P: Any point will give the same moment. In other words, a torque vector, unlike any other moment vector, is a "free vector"."​

both quotes from http://en.wikipedia.org/wiki/Couple_(mechanics)

 

[anmol21]

thanks a lot , that clears it up :)